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A company has been running a television advertisement for one of its new products and conducted a survey. Based on the results, the company concluded that an individual buys the product with probability 56% given that he or she saw the advertisement, and an individual buys the product with probability 8% given that he or she did not see it. Assume that one person buying the product is independent of another person buying the product.

A) What is the probability that a randomly selected individual from a group will buy the new product if twenty-five percent of the people in this group saw the advertisement?

B) Suppose the probability that an individual has seen the commercial is 0.25. What is the probability that at least one of five randomly selected individuals will buy the new product? (Hint: find the probability of the complement first, then use the complement rule.)

SOLUTION TO PART A =

$P(B\mid A) = .56\\ P(B\mid \lnot A) = .08\\ \\ P(A) = .25\\ P(\lnot A) = .75 \\ \\ P(B\mid A) = \frac{P (B \cap A)}{ P(A) }$

We have one unknown which comes out to be 0.14

$P(B\mid\lnot A) = \frac{P(B \cap\lnot A)}{P(\lnot A)}$

We have one unknown and we solve for it

For the final answer we add the two probs together

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    I got Part A have no idea about part B. The answer for part A is 0.2 – 2017-01-31

1 Answers 1

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Let X be an event where someone buys the product and Y an event where someone watches the ads. A) Probability of a randomly selected individual buys the product = $$P(X) = P(X|Y)*P(Y) + P(X|Y^{C})*(1-P(Y))$$

B) Probability of at least one of five randomly selected people buys the product = 1 - probability of none of the five people buys the product. $$1 - P(X^{C})^{5}$$