A large department store wants to study the purchasing habits of its customers for three specific products,

a, b,

c. The data given in the following table come from a market research that the store conducted and show the proportions of customers who purchase one or more among the three products during a specific period.

Assuming that these proportions reflect the probability for any customer to buy these product(s), calculate the probability that a customer (i) buys product a given (s)he has bought at least one of products b and c;
(ii) buys at least one of products b and c if (s)he has bought product a;
(iii) buys product a if we know that (s)he has bought at least one of the three products

a, b, and c.

Transcribed Image Text:

Product Percentage of buyers a 0.25 b 0.40 C 0.12 a & b 0.17 a & c 0.10 b & c 0.07 a,b & c 0.05