from a group of 6 men and 4 women , a committe of 3 is to be selected at random. find p(at least 2 woman)my answer is 1/6 if wrong give right answer and show the work please thank you
To find the probability of selecting at least 2 women from a committee of 3 people, we need to consider the total number of possible outcomes and the number of favorable outcomes.
First, let's calculate the total number of possible outcomes. We need to select 3 people from a group of 6 men and 4 women, which can be done using combinations. The total number of possible outcomes can be calculated as:
Total number of outcomes = C(10, 3) = 10! / (3! * (10 - 3)!) = 10! / (3! * 7!) = (10 * 9 * 8) / (3 * 2 * 1) = 120.
Now, let's calculate the number of favorable outcomes, i.e., the number of ways to select at least 2 women from the committee.
Case 1: Selecting 2 women and 1 man:
Number of ways = C(4, 2) * C(6, 1) = (4! / (2! * (4 - 2)!) * 6! / (1! * (6 - 1)!)) = (4 * 3 / (2 * 1)) * 6 = 18 * 6 = 108.
Case 2: Selecting 3 women:
Number of ways = C(4, 3) = 4.
Therefore, the total number of favorable outcomes = 108 + 4 = 112.
Now, calculate the probability by dividing the total number of favorable outcomes by the total number of possible outcomes:
P(at least 2 women) = Number of favorable outcomes / Total number of outcomes = 112 / 120 = 28 / 30 = 14 / 15.
So, the correct answer is 14/15, not 1/6.