Q&A Hero

Q: Refer to Exhibit 5-11. The probability that there are 8 occurrences in ten minutes is a. .0241 b. .0771 c. .1126 d. .9107

Q: Refer to Exhibit 5-11. The expected value of the random variable xisa. 2b. 5.3c. 10d. 2.30

Q: Refer to Exhibit 5-11. The appropriate probability distribution for the random variable isa. discreteb. continuousc. either a or b depending on how the interval is definedd. not enough information is given

Q: Exhibit 5-11The random variable xis the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3.Refer to Exhibit 5-11. The random variable xsatisfies which of the following probability distributions?a. normalb. Poissonc. binomiald. Not enough information is given to answer this question.

Q: In the textile industry, a manufacturer is interested in the number of blemishes or flaws occurring in each 100 feet of material. The probability distribution that has the greatest chance of applying to this situation is thea. normal distributionb. binomial distributionc. Poisson distributiond. uniform distribution

Q: When using Excel's POISSON function, one should choose TRUE for the third input if a. a probability is desired b. a cumulative probability is desired c. the expected value is desired d. the correct answer is desired

Q: Excel's POISSON function has how many inputs? a. 2 b. 3 c. 4 d. 5

Q: Excel's POISSON function can be used to compute a. bin width for histograms b. Poisson probabilities c. cumulative Poisson probabilities d. Both Poisson probabilities and cumulative Poisson probabilities are correct.

Q: When dealing with the number of occurrences of an event over a specified interval of time or space and when the occurrence or nonoccurrence in any interval is independent of the occurrence or nonoccurrence in any other interval, the appropriate probability distribution is a a. binomial distribution b. Poisson distribution c. normal distribution d. hypergeometric probability distribution

Q: The Poisson probability distribution is used witha. a continuous random variableb. a discrete random variablec. either a continuous or discrete random variabled. any random variable

Q: The Poisson probability distribution is a a. continuous probability distribution b. discrete probability distribution c. uniform probability distribution d. normal probability distribution

Q: Refer to Exhibit 5-10. The variance of the number of days Pete will catch fish is a. .16 b. .48 c. .8 d. 2.4

Q: Refer to Exhibit 5-10. The expected number of days Pete will catch fish is a. .6 b. .8 c. 2.4 d. 3

Q: Refer to Exhibit 5-10. The probability that Pete will catch fish on one day or less is a. .008 b. .096 c. .104 d. .8

Q: Refer to Exhibit 5-10. The probability that Pete will catch fish on exactly one day is a. .008 b. .096 c. .104 d. .8

Q: Exhibit 5-10The probability that Pete will catch fish on a particular day when he goes fishing is 0.8. Pete is going fishing 3 days next week.Refer to Exhibit 5-10. What is the random variable in this experiment?a. the 0.8 probability of catching fishb. the 3 daysc. the number of days out of 3 that Pete catches fishd. the number of fish in the body of water

Q: Refer to Exhibit 5-9. The probability that there are no females in the sample isa. 0.0778b. 0.7780c. 0.5000d. 0.3456

Q: Refer to Exhibit 5-9. The probability that the sample contains 2 female voters isa. 0.0778b. 0.7780c. 0.5000d. 0.3456

Q: Exhibit 5-9Forty percent of all registered voters in a national election are female. A random sample of 5 voters is selected.Refer to Exhibit 5-9. What is the random variable in this experiment?a. the 40% of female registered votersb. the random sample of 5 votersc. the number of female voters out of 5d. the number of registered voters in the nation

Q: Refer to Exhibit 5-8. What is the probability that among the students in the sample at least 6 are male?a. 0.0413b. 0.0079c. 0.0007d. 0.0499

Q: Refer to Exhibit 5-8. What is the probability that among the students in the sample at least 7 are female? a. 0.1064 b. 0.0896 c. 0.0168 d. 0.8936

Q: Refer to Exhibit 5-8. What is the probability that among the students in the sample exactly two are female? a. 0.0896 b. 0.2936 c. 0.0413 d. 0.0007

Q: Exhibit 5-8The student body of a large university consists of 60% female students. A random sample of 8 students is selected.Refer to Exhibit 5-8. What is the random variable in this experiment?a. the 60% of female studentsb. the random sample of 8 studentsc. the number of female students out of 8d. the student body size

Q: Twenty percent of the students in a class of 100 are planning to go to graduate school. The standard deviation of this binomial distribution isa. 20b. 16c. 4d. 2

Q: Assume that you have a binomial experiment with p= 0.4 and a sample size of 50. The variance of this distribution is a. 20 b. 12 c. 3.46 d. Not enough information is given to answer this question.

Q: An investment advisor recommends the purchase of shares in Infogenics, Inc. He has made the following predictions:P(Stock goes up 20% | Rise in GDP) = .6P(Stock goes up 20% | Level GDP) = .5P(Stock goes up 20% | Fall in GDP) = .4An economist has predicted that the probability of a rise in the GDP is 30%, whereas the probability of a fall in the GDP is 40%.a. Draw a tree diagram to represent this multiple-step experiment.b. What is the probability that the stock will go up 20%?c. We have been informed that the stock has gone up 20%. What is the probability of a rise or fall in the GDP?

Q: Super Cola sales breakdown as 80% regular soda and 20% diet soda. Men purchase 60% of the regular soda, but only 30% of the diet soda. If a woman purchases Super Cola, what is the probability that it is a diet soda?

Q: Safety Insurance Company has compiled the following statistics. For any one-year period:P(accident | male driver under 25) = .22P(accident | male driver over 25) = .15P(accident | female driver under 25) = .16P(accident | female driver over 25) = .14The percentage of Safety's policyholders in each category is:Male Under 25 20%Male Over 25 40%Female Under 25 10%Female Over 25 30%a. What is the probability that a randomly selected policyholder will have an accident within the next year?b. Given that a driver has an accident, what is the probability the driver is a male over 25?c. Given that a driver has no accident, what is the probability the driver is a female?

Q: Global Airlines operates two types of jet planes: jumbo and ordinary. On jumbo jets, 25% of the passengers are on business while on ordinary jets 30% of the passengers are on business. Of Global's air fleet, 40% of its capacity is provided on jumbo jets. (Hint: you have been given two conditional probabilities.)a. What is the probability a randomly chosen business customer flying with Global is on a jumbo jet?b. What is the probability a randomly chosen non-business customer flying with Global is on an ordinary jet?

Q: An accounting firm has noticed that of the companies it audits, 85% show no inventory shortages, 10% show small inventory shortages and 5% show large inventory shortages. The firm has devised a new accounting test for which it believes the following probabilities hold:P(company will pass test | no shortage) = .90P(company will pass test | small shortage) = .50P(company will pass test | large shortage) = .20a. If a company being audited fails this test, what is the probability of a large or small inventory shortage?b. If a company being audited passes this test, what is the probability of no inventory shortage?

Q: The Board of Directors of Bidwell Valve Company has made the following estimates for the upcoming year's annual earnings:P(earnings lower than this year) = .30P(earnings about the same as this year) = .50P(earnings higher than this year) = .20After talking with union leaders, the human resource department has drawn the following conclusions:P(Union will request wage increase | lower earnings next year) = .25P(Union will request wage increase | same earnings next year) = .40P(Union will request wage increase | higher earnings next year) = .90a. Calculate the probability that the company earns the same as this year and the union requests a wage increase.b. Calculate the probability that the company has higher earnings next year and the union does not request a wage increase.c. Calculate the probability that the union requests a wage increase.

Q: A market study taken at a local sporting goods store showed that of 20 people questioned, 6 owned tents, 10 owned sleeping bags, 8 owned camping stoves, 4 owned both tents and camping stoves, and 4 owned both sleeping bags and camping stoves.Let Event A= owns a tent, Event B= owns a sleeping bag, Event C= owns a camping stove,and Sample Space = 20 people questioned.a. Find P(A), P(B), P(C), P(AC), P(BC).b. Are the events Aand Cmutually exclusive? Explain briefly.c. Are the events Band Cindependent events? Explain briefly.d. If a person questioned owns a tent, what is the probability he also owns a camping stove?e. If two people questioned own a tent, a sleeping bag, and a camping stove, how many own only a camping stove?f. Is it possible for 3 people to own both a tent and a sleeping bag, but not a camping stove?

Q: In a city, 60% of the residents live in houses and 40% of the residents live in apartments. Of the people who live in houses, 20% own their own business. Of the people who live in apartments, 10% own their own business. If a person owns his or her own business, find the probability that he or she lives in a house.

Q: Thirty-five percent of the students who enroll in a statistics course go to the statistics laboratory on a regular basis. Past data indicates that 40% of those students who use the lab on a regular basis make a grade of B or better. On the other hand, 10% of students who do not go to the lab on a regular basis make a grade of B or better. If a particular student made an A, determine the probability that she or he used the lab on a regular basis.

Q: In a recent survey in a Statistics class, it was determined that only 60% of the students attend class on Fridays. From past data it was noted that 98% of those who went to class on Fridays pass the course, while only 20% of those who did not go to class on Fridays passed the course.a. What percentage of students is expected to pass the course?b. Given that a person passes the course, what is the probability that he/she attended classes on Fridays?

Q: A machine is used in a production process. From past data, it is known that 97% of the time the machine is set up correctly. Furthermore, it is known that if the machine is set up correctly, it produces 95% acceptable (non-defective) items. However, when it is set up incorrectly, it produces only 40% acceptable items.a. An item from the production line is selected. What is the probability that the selected item is non-defective?b. Given that the selected item is non-defective, what is the probability that the machine is set up correctly?c. What method of assigning probabilities was used here?

Q: A survey of business students who had taken the Graduate Management Admission Test (GMAT) indicated that students who have spent at least five hours studying GMAT review guides have a probability of 0.85 of scoring above 400. Students who do not spend at least five hours reviewing have a probability of 0.65 of scoring above 400. It has been determined that 70% of the business students spent at least five hours reviewing for the test.a. Find the probability of scoring above 400.b. Find the probability that given a student scored above 400, he/she spent at least five hours reviewing for the test.

Q: A statistics professor has noted from past experience that a student who follows a program of studying two hours for each hour in class has a probability of 0.9 of getting a grade of C or better, while a student who does not follow a regular study program has a probability of 0.2 of getting a C or better. It is known that 70% of the students follow the study program. Find the probability that if a student who has earned a C or better grade, he/she followed the program.

Q: A corporation has 15,000 employees. Sixty-two percent of the employees are male. Twenty-three percent of the employees earn more than $30,000 a year. Eighteen percent of the employees are male and earn more than $30,000 a year.a. If an employee is taken at random, what is the probability that the employee is male?b. If an employee is taken at random, what is the probability that the employee earns more than $30,000 a year?c. If an employee is taken at random, what is the probability that the employee is male and earns more than $30,000 a year?d. If an employee is taken at random, what is the probability that the employee is male or earns more than $30,000 a year or both?e. The employee taken at random turns out to be male. Compute the probability that he earns more than $30,000 a year.f. Are being male and earning more than $30,000 a year independent?

Q: An applicant has applied for positions at Company A and Company B. The probability of getting an offer from Company A is 0.4, and the probability of getting an offer from Company B is 0.3. Assuming that the two job offers are independent of each other, what is the probability thata. the applicant gets an offer from both companies?b. the applicant will get at least one offer?c. the applicant will not be given an offer from either company?d. Company A does not offer the applicant a job, but Company B does?

Q: As a company manager for Claimstat Corporation there is a 0.40 probability that you will be promoted this year. There is a 0.72 probability that you will get a promotion or a raise. The probability of getting a promotion and a raise is 0.25.a. If you get a promotion, what is the probability that you will also get a raise?b. What is the probability of getting a raise?c. Are getting a raise and being promoted independent events? Explain using probabilities.d. Are these two events mutually exclusive? Explain using probabilities.

Q: The probability of an economic decline in the year 2001 is 0.23. There is a probability of 0.64 that we will elect a republican president in the year 2000. If we elect a republican president, there is a 0.35 probability of an economic decline. Let "D" represent the event of an economic decline, and "R" represent the event of election of a Republican president.a. Are "R" and "D" independent events?b. What is the probability of electing a Republican president in 2000 and an economic decline in the year 2001?c. If we experience an economic decline in the year 2001, what is the probability that a Republican president will have been elected in the year 2000?d. What is the probability of economic decline in 2001 or a Republican president elected in the year 2000 or both?

Q: In the two upcoming basketball games, the probability that UTC will defeat Marshall is 0.63, and the probability that UTC will defeat Furman is 0.55. The probability that UTC will defeat both opponents is 0.3465.a. What is the probability that UTC will defeat Furman given that they defeat Marshall?b. What is the probability that UTC will win at least one of the games?c. What is the probability of UTC winning both games?d. Are the outcomes of the games independent? Explain and substantiate your answer.

Q: Assume you have applied for two scholarships, a Merit scholarship (M) and an Athletic scholarship (A). The probability that you receive an Athletic scholarship is 0.18. The probability of receiving both scholarships is 0.11. The probability of getting at least one of the scholarships is 0.3.a. What is the probability that you will receive a Merit scholarship?b. Are events A and M mutually exclusive? Why or why not? Explain.c. Are the two events, A and M, independent? Explain, using probabilities.d. What is the probability of receiving the Athletic scholarship given that you have been awarded the Merit scholarship?e. What is the probability of receiving the Merit scholarship given that you have been awarded the Athletic scholarship?

Q: Assume you have applied to two different universities (let's refer to them as Universities A and B) for your graduate work. In the past, 25% of students (with similar credentials as yours) who applied to University A were accepted, while University B accepted 35% of the applicants. Assume events are independent of each other.a. What is the probability that you will be accepted in both universities?b. What is the probability that you will be accepted to at least one graduate program?c. What is the probability that one and only one of the universities will accept you?d. What is the probability that neither university will accept you?

Q: Assume you are taking two courses this semester (A and B). Based on your opinion, you believe the probability that you will pass course A is 0.835; the probability that you will pass both courses is 0.276. You further believe the probability that you will pass at least one of the courses is 0.981.a. What is the probability that you will pass course B?b. Is the passing of the two courses independent events? Use probability information to justify your answer.c. Are the events of passing the courses mutually exclusive? Explain.d. What method of assigning probabilities did you use?

Q: Tammy is a general contractor and has submitted two bids for two projects (A and B). The probability of getting project A is 0.65. The probability of getting project B is 0.77. The probability of getting at least one of the projects is 0.90.a. What is the probability that she will get both projects?b. Are the events of getting the two projects mutually exclusive? Explain, using probabilities.c. Are the two events independent? Explain, using probabilities.

Q: Sixty percent of the student body at UTC is from the state of Tennessee (T), 30% percent are from other states (O), and the remainder is international students (I). Twenty percent of students from Tennessee live in the dormitories, whereas 50% of students from other states live in the dormitories. Finally, 80% of the international students live in the dormitories.a. What percentage of UTC students lives in the dormitories?b. Given that a student lives in the dormitory, what is the probability that she/he is an international student?c. Given that a student does notlive in the dormitory, what is the probability that she/he is an international student?

Q: In a random sample of UTC students 50% indicated they are business majors, 40% engineering majors, and 10% other majors. Of the business majors, 60% were females; whereas, 30% of engineering majors were females. Finally, 20% of the other majors were female.a. What percentage of students in this sample was female?b. Given that a person is female, what is the probability that she is an engineering major?

Q: Six vitamin and three sugar tablets identical in appearance are in a box. One tablet is taken at random and given to Person A. A tablet is then selected and given to Person B.What is the probability thata. Person A was given a vitamin tablet?b. Person B was given a sugar tablet given that Person A was given a vitamin tablet?c. neither was given vitamin tablets?d. both were given vitamin tablets?e. exactly one person was given a vitamin tablet?f. Person A was given a sugar tablet and Person B was given a vitamin tablet?g. Person A was given a vitamin tablet and Person B was given a sugar tablet?

Q: On a recent holiday evening, a sample of 500 drivers was stopped by the police. Three hundred were under 30 years of age. A total of 250 were under the influence of alcohol. Of the drivers under 30 years of age, 200 were under the influence of alcohol.Let A be the event that a driver is under the influence of alcohol.Let Y be the event that a driver is less than 30 years old.a. Determine P(A) and P(Y).b. What is the probability that a driver is under 30 and notunder the influence of alcohol?c. Given that a driver is notunder 30, what is the probability that he/she is under the influence of alcohol?d. What is the probability that a driver is under the influence of alcohol if we know the driver is under 30?e. Show the joint probability table.f. Are A and Y mutually exclusive events? Explain.g. Are A and Y independent events? Explain.

Q: A small town has 5,600 residents. The residents in the town were asked whether or not they favored building a new bridge across the river. You are given the following information on the residents' responses, broken down by gender.MenWomenTotalIn Favor1,4002801,680Opposed8403,0803,920Total2,2403,3605,600Let: M be the event a resident is a manW be the event a resident is a womanF be the event a resident is in favorP be the event a resident is opposeda. Find the joint probability table.b. Find the marginal probabilities.c. What is the probability that a randomly selected resident is a man and is in favor of building the bridge?d. What is the probability that a randomly selected resident is a man?e. What is the probability that a randomly selected resident is in favor of building the bridge?f. What is the probability that a randomly selected resident is a man or in favor of building the bridge or both?g. A randomly selected resident turns out to be male. Compute the probability that he is in favor of building the bridge.

Q: The following table shows the number of students in three different degree programs and whether they are graduate or undergraduate students:Degree ProgramUndergraduateGraduateTotalBusiness15050200Engineering15025175Arts & Sciences10025125Total400100500a. What is the probability that a randomly selected student is an undergraduate?b. What percentage of students is engineering majors?c. If we know that a selected student is an undergraduate, what is the probability that he or she is a business major?d. A student is enrolled in the Arts and Sciences school. What is the probability that the student is an undergraduate student?e. What is the probability that a randomly selected student is a graduate Business major?

Q: A survey of a sample of business students resulted in the following information regarding the genders of the individuals and their major.MajorGenderManagementMarketingOthersTotalMale40103080Female302070120Total7030100200a. What is the probability of selecting an individual who is majoring in Marketing?b. What is the probability of selecting an individual who is majoring in Management, given that the person is female?c. Given that a person is male, what is the probability that he is majoring in Management?d. What is the probability of selecting a male individual?

Q: A bank has the following data on the gender and marital status of 200 customers.MaleFemaleSingle2030Married10050a. What is the probability of finding a single female customer?b. What is the probability of finding a married male customer?c. If a customer is female, what is the probability that she is single?d. What percentage of customers is male?e. If a customer is male, what is the probability that he is married?f. Are gender and marital status mutually exclusive?g. Is marital status independent of gender? Explain using probabilities.

Q: A government agency has 6,000 employees. The employees were asked whether they preferred a four-day work week (10 hours per day), a five-day work week (8 hours per day), or flexible hours. You are given information on the employees' responses broken down by gender.MaleFemaleTotalFour days300600900Five days1,2001,5002,700Flexible3002,1002,400Total1,8004,2006,000a. What is the probability that a randomly selected employee is a man and is in favor of a four-day work week?b. What is the probability that a randomly selected employee is female?c. A randomly selected employee turns out to be female. Compute the probability that she is in favor of flexible hours.d. What percentage of employees is in favor of a five-day work week?e. Given that a person is in favor of flexible time, what is the probability that the person is female?f. What percentage of employees is male and in favor of a five-day work week?

Q: You are given the following information on Events A, B, C, and D.P(A) = .4P(A D) = .6P(A C) = .04P(B) = .2P(AB) = .3P(A D) = .03P(C) = .1a. Compute P(D).b. Compute P(AB).c. Compute P(AC).d. Compute the probability of the complement of C.e. Are A and B mutually exclusive? Explain your answer.f. Are A and B independent? Explain your answer.g. Are A and C mutually exclusive? Explain your answer.h. Are A and C independent? Explain your answer.

Q: Assume two events A and B are mutually exclusive and, furthermore, P(A) = 0.2 and P(B) = 0.4.a. Find P(A B).b. Find P(A B).c. Find P(AB).

Q: Two of the cylinders in an eight-cylinder car are defective and need to be replaced. If two cylinders are selected at random, what is the probability thata. both defective cylinders are selected?b. no defective cylinder is selected?c. at least one defective cylinder is selected?

Q: A very short quiz has one multiple-choice question with five possible choices (a, b, c, d, e) and one true or false question. Assume you are taking the quiz but do not have any idea what the correct answer is to either question, but you mark an answer anyway.a. What is the probability that you have given the correct answer to both questions?b. What is the probability that only one of the two answers is correct?c. What is the probability that neither answer is correct?d. What is the probability that only your answer to the multiple-choice question is correct?e. What is the probability that you have only answered the true or false question correctly?

Q: Assume that in your hand you hold an ordinary six-sided die and a dime. You toss both the die and the dime on a table.a. What is the probability that a head appears on the dime and a six on the die?b. What is the probability that a tail appears on the dime and any number more than 3 on the die?c. What is the probability that a number larger than 2 appears on the die?

Q: An experiment consists of throwing two six-sided dice and observing the number of spots on the upper faces. Determine the probability thata. the sum of the spots is 3.b. each die shows four or more spots.c. the sum of the spots is not 3.d. neither a one nor a six appear on each die.e. a pair of sixes appear.f. the sum of the spots is 7.

Q: The results of a survey of 800 married couples and the number of children they had is shown below.Number of ChildrenProbability00.05010.12520.60030.15040.05050.025If a couple is selected at random, what is the probability that the couple will havea. Less than 4 children?b. More than 2 children?c. Either 2 or 3 children?

Q: The sales records of a real estate agency show the following sales over the past 200 days:Number of Houses SoldNumber of Days06018024031644a. How many sample points are there?b. Assign probabilities to the sample points and show their values.c. What is the probability that the agency will not sell any houses in a given day?d. What is the probability of selling at least 2 houses?e. What is the probability of selling 1 or 2 houses?f. What is the probability of selling less than 3 houses?

Q: A committee of 4 is to be selected from a group of 12 people. How many possible committees can be selected?

Q: A student has to take 7 more courses before she can graduate. If none of the courses are prerequisites to others, how many groups of three courses can she select for the next semester?

Q: A company plans to interview 10 recent graduates for possible employment. The company has three positions open. How many groups of three can the company select?

Q: All the employees of ABC Company are assigned ID numbers. The ID number consists of the first letter of an employee's last name, followed by four numbers.a. How many possible different ID numbers are there?b. How many possible different ID numbers are there for employees whose last name starts with an "A"?

Q: ABCDE1PriorConditionalJointPosterior2EventProbabilityProbabilityProbabilityProbability3A10.450.220.0994A20.550.160.08850.187For the Excel worksheet above, which of the following formulas would correctly calculate the posterior probability for cell E3?a. =SUM(B3:D3)b. =D3/$D$5c. =D5/$D$3d. B3/C3+D3

Q: ABCDE1PriorConditionalJoint2EventProbabilityProbabilityProbability3A10.250.31For the Excel worksheet above, which of the following formulas would correctly calculate the joint probability for cell D3?a. =SUM(B3:C3)b. B3+C3c. B3/C3d. =B3*C3

Q: Initial estimates of the probabilities of events are known as a. sets b. posterior probabilities c. conditional probabilities d. prior probabilities

Q: Bayes' theorem is used to compute a. the prior probabilities b. the union of events c. both the prior probabilities and theunion of events d. the posterior probabilities

Q: The probability of the occurrence of event A in an experiment is 1/3. If the experiment is performed 2 times and event A did not occur, then on the third trial event A a. must occur b. may occur c. could not occur d. has a 2/3 probability of occurring

Q: A perfectly balanced coin is tossed 6 times and tails appears on all six tosses. Then, on the seventh trial a. tails cannot appear b. heads has a larger chance of appearing than tails c. tails has a better chance of appearing than heads d. None of the other answers is correct.

Q: If a penny is tossed three times and comes up heads all three times, the probability of heads on the fourth trial is a. smaller than the probability of tails b. larger than the probability of tails c. 1/16 d. None of the other answers is correct.

Q: If a penny is tossed four times and comes up heads all four times, the probability of heads on the fifth trial is a. zero b. 1/32 c. 0.5 d. larger than the probability of tails

Q: If a coin is tossed three times, the likelihood of obtaining three heads in a row is a. zero b. 0.500 c. 0.875 d. 0.125

Q: A six-sided die is tossed 3 times. The probability of observing three ones in a row is a. 1/3 b. 1/6 c. 1/27 d. 1/216

Q: If A and B are independent events with P(A) = 0.05 and P(B) = 0.65, then P(AB) =a. 0.05b. 0.0325c. 0.65d. 0.8

Q: Events A and B are mutually exclusive. Which of the following statements is also true? a. A and B are also independent. b. P(A B) = P(A)P(B) c. P(A B) = P(A) + P(B) d. P(A B) = P(A) + P(B)