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Political scientists want to determine the probability of exactly 3 out of the next 5 voters they meet approving a proposal.

If the sample probability of the voters approving the proposal is 50%, the number of trials is and the number of successful trials is .

The probability that 3 out of the next 5 voters approving the proposal is

1 Answer

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Answer:

Probability that 3 out of the next 5 voters approving the proposal is 0.3125.

Explanation:

We are given that the sample probability of the voters approving the proposal is 50% and Political scientists want to determine the probability of exactly 3 out of the next 5 voters they meet approving a proposal.

The above situation can be represented through binomial distribution;


P(X=r) = \binom{n}{r} * p^(r) * (1-p)^(n-r) ; x = 0,1,2,3,.....

where, n = number of trials (samples) taken = 5

r = number of success = exactly 3

p = probability of success which in our question is probability of

the voters approving the proposal, i.e; p = 50%

Let X = Number of voters approving the proposal

So, X ~ Binom(n = 5 , p = 0.50)

Now, Probability that 3 out of the next 5 voters approving the proposal is given by = P(X = 3)

P(X = 3) =
\binom{5}{3} * 0.50^(3) * (1-0.50)^(5-3)

=
10 * 0.50^(3) * 0.50^(2)

= 0.3125

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