Question

Sixty-five percent of men consider themselves knowledgeable football fans. if 12 men are randomly selected, find the probability that exactly four of them will consider themselves knowledgeable fans.

Answer 1

P(x)= 0.0198

Explanation:

Given : 65% men are knowledgeable football fans, 12 are randomly selected ,

To find : Probability that exactly four of them will consider themselves knowledgeable fans.

Solution : Let P is the success rate = 65% = 0.65

Let Q is the failure rate = 100-65= 35%= 0.35

Let n be the total number of fans selected = 12

Let r be the probability of getting exactly four = 4

Formula used : The binomial probability

`P(x)= (n!)/((n-r)!r!)P^rQ^(n-r)`

putting values in the formula we get ,

`P(x)= (12!)/((12-4)!4!)(0.65)^4(0.35)^(12-4)`

`P(x)= (495)(0.1785)(o.ooo22 )`

P(x)= 0.0198