# Question: A sporting goods store sells two competing brands of exercise

A sporting goods store sells two competing brands of exercise bicycles. Let X1 and X2 be the numbers of the two brands sold on a typical day at this store. Based on available historical data, the conditional probability distribution of X1 given X2 is assessed as shown in the file S04_35.xlsx. The marginal distribution of X2 is given in the bottom row of the table.

a. Are X1 and X2 independent random variables? Explain why or why not.

b. What is the probability of observing the sale of exactly one brand 1 bicycle and exactly one brand 2 bicycle on the same day at this store?

c. What is the probability of observing the sale of at least one brand 1 bicycle on a given day at this store?

d. What is the probability of observing the sale of no more than two brand 2 bicycles on a given day at this store?

e. Given that no brand 2 bicycles are sold on a given day, what is the likelihood of observing the sale of at least one brand 1 bicycle at this store?

a. Are X1 and X2 independent random variables? Explain why or why not.

b. What is the probability of observing the sale of exactly one brand 1 bicycle and exactly one brand 2 bicycle on the same day at this store?

c. What is the probability of observing the sale of at least one brand 1 bicycle on a given day at this store?

d. What is the probability of observing the sale of no more than two brand 2 bicycles on a given day at this store?

e. Given that no brand 2 bicycles are sold on a given day, what is the likelihood of observing the sale of at least one brand 1 bicycle at this store?

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