Answer to Question #245574 in Statistics and Probability for Janith

Question

The probability that a person supports party ‘A’ is 0.86. Find the probability that in a randomly selected 9 voters there are,
1)Exactly 3 who supports party A
2)More than 5 who supports party A

Answer 1

This is a binomial distribution with n=9, p=0.86.

1) $P(X=3)=C_9^30.86^3(1-0.86)^{9-3}=0.0004.$

2) $P(X>5)=\Sigma_{i=6}^9 P(X=i)=\Sigma_{i=6}^9C_9^i0.86^i(1-0.86)^{9-i}=0.9731.$