Question

Consider the population of voters described in Example 3.6. Suppose that there are N = 5000 voters in the population, 40% 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 .40. 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) = .4. What is P(B| the first trial is S)? Does this conditional probability differ markedly from P(B)?

Answer 1

Explanation:

We know that P( S ) = 0.4

Probability of occurance of event B can be calculated as follows

This probability consists of two elements

1 ) Probability of first two trial becoming successful

= .4 x .4 = .16

2 ) a ) Probability of first trial becoming failure = 1-.4

= 0.6

b ) probability of second trial becoming success = .4

Probability of occurance of both a ) and b ) event simultaneously one after another.

= 0.6 x 0.4

.24

Total probability of .first two trials becoming both successes or the first trial is a failure and the second is a success is

.16+ .24 = .4

Hence

P(B) = .4