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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 |
Given that no brand 2 bats are sold on a given day, what is the probability of observing the sale of at least one brand 1 bicycle at this sporting goods store?
Answer
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