1. Drake Marketing and Promotions has randomly surveyed 200 men who watch profes

Question

1. Drake Marketing and Promotions has randomly surveyed 200 men who watch professional sports. The men were separated according to their educational level (college degree or not) and whether they preferred the NBA or the National Football League (NFL). The results of the survey are shown: ollege Degree 0 o College Degree orts Preference BA FL What is the joint probability that a randomly selected survey participant has a college degree and prefers the NBA? 0.2 2. A study was recently done in which 500 people were asked to indicate their preferences for one of three products The following table shows the breakdown of the responses by gender of the respondents Product Preference Gender Male Female 80 200 20 70 10 120 Based on the relative frequency assessment method, what is probability that a person in the study will prefer product A? 0.56 3. Several customers at the Sweet Haven Chocolate Company have complained about quality. It seems there are several partially covered chocolates being found in boxes. The defective chocolates should have been caught when the boxes were packed. Use Baves' Theorem to determine which clerk is most likely responsible for the boxes that raised the complaints? Clerk Boxes Packed 0.40 0.30 0.30 Defective Rate 0.02 0.025 0.015 2

Explanation / Answer

1:

Following table shows the row total and column total:

Out of 200 paticipants, 40 have college degree and NBA so

P(college degree and NBA) = 40/200 = 0.20

2:

Out of 500 people, 80+200 = 280 prefer product A so

P(prefer product A) = 280 /500 = 0.56

3:

Here we have

P(D|C1) = 0.02, P(D|C2 ) = 0.025, P(D|C3) = 0.015

The probability that a box has defective is

P(D) = P(D|C1)P(C1) + P(D|C2)P(C2) + P(D|C3)P(C3) = 0.02 * 0.40 +0.025 *0.30 +0.015*0.30 = 0.008 + 0.0075 + 0.0045 = 0.02

So by the Baye's theorem we have

P(C1|D) = [P(D|C1) P(C1) ] / P(D) = 0.008 / 0.02 = 0.40

P(C2|D) = [P(D|C2) P(C2) ] / P(D) = 0.0075 / 0.02 = 0.375

P(C3|D) = [P(D|C3) P(C3) ] / P(D) = 0.0045 / 0.02 = 0.225

That is clerk one is most likely responsible for the boxes that raised the complaints.

College degree No college Degree Total NBA 40 55 95 NFL 10 95 105 Total 50 150 200

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