Question

consider a population of voters. suppose that that there are n=1000 voters in the population, 30% of whom favor jones. identify the event favors jones as a success s. it is evident that the probability of s on trial 1 is 0.30. consider the event b that s occurs on the second trial. then b can occur two ways: the first two trials are both successes or the first trial is a failure and the second is a success. show that p(b) = 0.3

Answer 1

P(B)=0.30

Explanation:

Out of 1000 Voters, 30% favor Jones.

Event S=Favors Jones on First Trial

Event B=S occurs on Second Trial

P(S)=0.30

P(S')=1-0.30=0.70

Event B could occur in two ways

1. The first two trials are a success
2. The first trial is a failure and the second trial is a success.

Therefore,

P(B)=P(SS)+P(S'S)

=(0.3X0.3)+(0.7X0.3)

=0.09+0.21

=0.3

Therefore, the probability of event B(that event S occurs on the second trial), P(B)=0.30.