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In: Statistics and Probability

Statistic Question Market research for an online electronics retailer showed that 23% of its customers purchased...

Statistic Question

Market research for an online electronics retailer showed that 23% of its customers purchased a smartphone. 12% of these smartphone customers used an online payment system (such as Paypal) to pay for their purchases, i.e., given that a customer purchased a smartphone, the probability was 12% that he/she used an online payment system to pay. In general, 8% of the customers used an online payment system to pay for their purchases.

a.What percent of customers did not purchase a smartphone?

b.What percent of customers purchased a smartphone and used an online payment system to pay?

c.What percent of customers purchased a smartphone or used an online payment system to pay?

d.Are the events “purchased a smartphone” and “used an online payment system to pay” mutually exclusive? Why or why not?

e.Are the events “purchased a smartphone” and “used an online payment system to pay” independent? Use probabilities to justify your answer.

Expert Solution

Solution: a.What percent of customers did not purchase a smartphone?

Answer: %

b.What percent of customers purchased a smartphone and used an online payment system to pay?

Answer: We are given that 23% of customers purchased online and of these 23% of customers 12% paid online.

Therefore the percent of customers purchased a smartphone and used an online payment system to pay is %

c.What percent of customers purchased a smartphone or used an online payment system to pay?

Answer: Let X be the probability that a customer purchased a smartphone and is given by:

and Let Y be the probability that a customer used an online payment system to pay and is given below:

Therefore the percent of customers purchased a smartphone or used an online payment system to pay is 28.24%

d.Are the events “purchased a smartphone” and “used an online payment system to pay” mutually exclusive? Why or why not?

Answer: The events Purchasing a smartphone and making an online payment aren't mutually exclusive, because we could have purchased a smartphone and paid online.

e.Are the events “purchased a smartphone” and “used an online payment system to pay” independent? Use probabilities to justify your answer.

Answer: Purchased a smartphone and used an online payment system can be independent only if

We know that

Since , therefore the events "purchased a smartphone" and "used an online payment system to pay" are not independent.

orchestra answered 2 years ago

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