Sixty - five percent of men consider themselves knowledgeable football fans.

If 10 men are randomly selected, find the probability that exactly six of them will consider themselves knowledgeable fans.

a) 0.65 b) 0.069 c) 0.600 d) 0.238

Answer: d) 0.238

Step-by-step explanation:

We would assume binomial distribution for the number of men sampled. The formula for binomial distribution is expressed as

P (x = r) = nCr * q^ (n - r) * p^r

Where

p represents the probability of success.

q represents the probability of failure.

n represents the number of samples.

From the information given,

n = 10

p = 65% = 65/100 = 0.65

q = 1 - p = 1 - 0.65 = 0.35

The probability that exactly six of them will consider themselves knowledgeable fans is expressed as P (x = 6). It becomes

P (x = 6) = 10C6 * 0.35^ (10 - 6) * 0.65^6

P (x = 6) = 10C6 * 0.35^4 * 0.65^6

P (x = 6) = 0.238