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:Step-by-step explanation:We know that P( S ) = 0.4Probability of occurance of event B can be calculated as followsThis 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