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) ?

Question

Mathematics

Dominik Sparks

4 April, 19:05

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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Answers (1)

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Trystan Huang · Answer 1

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