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

This can be calculated using the binomial probability equation:

P = [n! / (n – r)! r!] p^r q^(n - r)

Where,

n = total number of men = 12

r = number of men who consider themselves knowledgeable fans = 4

p = probability of success = 65% = 0.65

q = probability of failure = 0.35

Substituting the given values:

P = (12! / 8!) * 0.65^(4) * 0.35^(8!)

P = 0.48 = 48%

Answer 2

Answer:

P(x)= 0.0198

Step-by-step 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

$P(x)= \frac{n!}{(n-r)!r!}P^rQ^{n-r}$

putting values in the formula we get ,

$P(x)= \frac{12!}{(12-4)!4!}(0.65)^4(0.35)^{12-4}$

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

 P(x)= 0.0198