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12 June, 20:12

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) ?

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  1. 12 June, 22:30
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    Step-by-step 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
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