Question

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.

Answer 1

Answer:

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