In a recent election there were 1000 eligible voters. They were asked to vote on two issues, A and B. The results were as follows: 100 people voted for A, 450 people voted for B, and 25 people voted for A and B. If one person is chosen at random from the 1000 eligible voters, find the following probabilities:

a. The person voted for A, given that he voted for B.

b. The person voted for B, given that he voted for A.

a) the probability is 1/4 (25%)

b) the probability is 1/18 (5.55%)

Step-by-step explanation:

a) defining the events A = the person voted for A and the event B = the person voted for B, then for conditional probability we can use the theorem of Bayes. Thus,

P (A/B) = P (A∩B) / P (A)

Where

P (A/B) = probability that the person voted for A, given that he voted for B

P (A∩B) = probability that the person voted for A and B

replacing values

P (A/B) = P (A∩B) / P (A) = 25/total / 100/total = 1/4 (25%)

b) similarly for B:

P (B/A) = P (A∩B) / P (B) = 25/total / 450/total = 1/18 (5.55%)

where

P (A/B) = probability that the person voted for B, given that he voted for A