Question

In a small voting precinct, 100 voters favor candidate A and 80 oppose candidate A. a)...

In a small voting precinct, 100 voters favor candidate A and 80 oppose candidate A.

a) What is the probability that a majority of a random sample of 3 voters will oppose candidate A?

b) Approximate the probability using a binomial probability.

c) Briefly explain why the approximated probability from (b) is close to the true probability

Math   Statistics-And-Probability   
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Answer #1

Total number of persons =100 + 80 = 180

The probability that a randomly selected voter will oppose candidate A

Let X denotes the number of voters who will  oppose candidate A in a random sample of 3 voters.

X ~ Binomial(n = 3, p = 0.44444)

The probability mass function of X is

The probability that a majority of a random sample of 3 voters will oppose candidate A

answers of a) and b) is same.

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