Question

An advertising agency notices that approximately 1 in 50 potential buyers of a product sees a given magazine ad, and 1 in 8 sees a corresponding ad on television. One in 100 sees both. One in 4 actually purchases the product after seeing the ad, 1 in 10 without seeing it. What is the probability that a randomly selected potential customer will purchase the product

Answer 1

Probability = 0.12025

Explanation:

P (Am) = 1/50 = 0.02 {Magazine ad}

P (At) = 1/8 = 0.125 {Television ad}

P (Am ∩ At ) = 1/100 = 0.01 {Both ads}

P (Am U At) = P (Am) + P (At) - P (Am ∩ At )

= 0.02 + 0.125 - 0.01

P (Am U At) = 0.135 {Person sees either ad}

P (Am' ∩ At') = 1 - P (Am U At)

P (Am' ∩ At') = 1 - 0.135 = 0.865 {Person sees none ad}

Prob (Purchase) = Prob (Purchase with ad) + Prob (purchase without ad)

P (P/ A) = 1/4 = 0.25 , P (P / A') = 1/10 = 0.1

P (P) = (0.25) (0.135) + (0.1) (0.865)

= 0.03375 + 0.0865

0.12025