Find the indicated probability. Round to four decimal places.
-The participants in a television quiz show are picked from a large pool of applicants with approximately equal numbers of men and women. Among the last 10 participants there have been
Only 2 women. If participants are picked randomly, what is the probability of getting 2 or fewer Women when 10 people are picked?
A)0.0547
B)0.0439
C)0.0107
D)0.0537

Question

Find the indicated probability. Round to four decimal places.
-The participants in a television quiz show are picked from a large pool of applicants with approximately equal numbers of men and women. Among the last 10 participants there have been
Only 2 women. If participants are picked randomly, what is the probability of getting 2 or fewer Women when 10 people are picked? 
A)0.0547
B)0.0439
C)0.0107
D)0.0537

Quizplus · Accepted Answer

This is a binomial probability problem where we are looking for the probability of getting 2 or fewer successes (women in this case) out of 10 trials (participants), with the probability of success on a single trial being 0.5 (since there are equal numbers of men and women). The formula for binomial probability is P(X = k) = (nCk) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, p is the probability of success on a single trial, and nCk is the binomial coefficient. To find the probability of getting 2 or fewer women, we sum the probabilities of getting exactly 0, 1, and 2 women. Calculating these probabilities and summing them gives a result that rounds to 0.0547, making option A correct.

Find the Indicated Probability