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Question
NARRBEGIN: SA_84_90A sporting goods store sells two competing brands of softball bats. Let
and 
be the numbers of the two brands sold on a typical day at the store. Based on the store historical data, the conditional probability distribution of given is assessed and provided in the table below. The marginal distribution of is also given in the bottom row of the table.Sales of Brand 1, Given sales of Brand 2
| = 0 | = 1 | = 2 | = 3 | |
| = 0 | 0.05 | 0.15 | 0.25 | 0.30 |
| = 1 | 0.10 | 0.25 | 0.55 | 0.57 |
| = 2 | 0.60 | 0.50 | 0.15 | 0.10 |
| = 3 | 0.25 | 0.10 | 0.05 | 0.03 |
| Marginal Distribution of | 0.20 | 0.30 | 0.30 | 0.20 |
What is the probability of observing the sale of no more than two brand 2 bats on a given day at this sporting goods store?
Answer
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