Use the general multiplication rule to find the indicated probability.
-Among the contestants in a competition are 44 women and 30 men. If 5 winners are randomly selected, what is the probability that they are all men?
A)0.13122
B)0.07432
C)0.14735
D)0.00885

Question

Use the general multiplication rule to find the indicated probability.
-Among the contestants in a competition are 44 women and 30 men. If 5 winners are randomly selected, what is the probability that they are all men? 
A)0.13122
B)0.07432
C)0.14735
D)0.00885

Quizplus · Accepted Answer

The probability of selecting all men can be calculated using the combination formula for selecting r items out of n, which is C(n, r) = n! / [r!(n-r)!], and then applying the general multiplication rule. The total number of ways to select 5 winners out of 74 (44 women + 30 men) contestants is C(74, 5). The number of ways to select 5 men out of 30 is C(30, 5). The probability is then the ratio of these two, P(all men) = C(30, 5) / C(74, 5). Calculating this gives a probability of approximately 0.00885.

Use the General Multiplication Rule to Find the Indicated Probability