Question

​Sixty-five percent of men consider themselves knowledgeable soccer fans. If 12 men are randomly​ selected, find the probability that exactly five of them will consider themselves knowledgeable fans. Round to the nearest thousandth.

Answer 1

Solution:

Given,

p = 95% = 0.65

1 - p = 1 - 0.65 = 0.35

n = 12

$url=https://latex.codecogs.com/gif.latex?%5Ctherefore&t=1576342873&ymreqid=50870fb5-0ab3-84d7-1c06-d40003012800&sig=CU2BvygA0n7nIitivElvoA--~C$ X follows the Binomial(12 , 0.65)

Using binomial probability formula ,

P(X = x) = (_n C _x) * p^x * (1 - p)^{n - x} ; x = 0 ,1 , 2 , ....., n

P(X = Exactly 5) = (₁₂ C ₅) * 0.65⁵ * (0.35)^{12 - 5} = [12!/(5! * 7!)] * 0.65⁵ * (0.35)⁷ = 0.059

P(X = Exactly 5) = 0.059