Question

A Committee of 3 people is to be chooson at random from 3 men and 2 wor Find the Piebability that a) All the 3 People choosen ale men. & 1 Pt the 3 People Chosen is a woman ​

Answer 1

The probability of choosing a committee of 3 people from 3 men and 2 women where all are men is 1/10, while the probability of having exactly one woman on the committee is 3/10.

Step-by-step explanation:

The question involves calculating probabilities for selecting a committee, which is a common task in combinatorics, a branch of mathematics. Specifically, the question is about finding the probability of certain gender compositions when choosing a committee.

Part a) All 3 chosen are men

The probability that all three people chosen are men is found by considering the number of ways to choose 3 men out of 3 (which is just 1 way), divided by the total number of ways to choose 3 people out of 5 (which is 10 ways). So, the probability is 1/10 or 0.1.

Part b) Exactly 1 of the 3 chosen is a woman

The probability that exactly 1 of the 3 people chosen is a woman can be calculated by multiplying together the number of ways to choose 1 woman out of 2, the number of ways to choose 2 men out of 3, and then dividing by the total number of ways to choose 3 people out of 5.

This gives us (2 choose 1) * (3 choose 2) / (5 choose 3) which is 3/10 or 0.3.