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)0.238
B)0.069
C)0.65
D)0.600

Question

Quizplus · Accepted Answer

This is a binomial probability problem where n = 10 (number of trials), k = 6 (number of successes), and p = 0.65 (probability of success on a single trial). The binomial probability formula is P(X = k) = (nCk) * p^k * (1-p)^(n-k), where nCk is the combination of n items taken k at a time. Plugging in the values: P(X = 6) = (10C6) * (0.65)^6 * (0.35)^4, which calculates to approximately 0.238.

Sixty-Five Percent of Men Consider Themselves Knowledgeable Football Fans