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The popularity rate of a political candidate is 57%. If 20 citizens are randomly selected, what...

The popularity rate of a political candidate is 57%. If 20 citizens are randomly selected, what is the probability that exactly 11 in the sample are in favor of this candidate?

0.038

0.213

0.507

0.174
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Answer #1

p(favour) = 0.57\\ q(not \,in \,favour) = 1-0.57 = 0.43\\ P(Exactly\,11\,in\,favour) = ^{20}C_{11} *p^{11}q^{20-11}\\ = ^{20}C_{11} *{0.57}^{11}*{0.43}^{9} = 0.1741988880

Hence , correct option is 0.174

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