Question

A club is choosing 2 members to serve on a committee. The club has

nominated 3 women and 3 men. Based on chance alone, what is the
probability no women are chosen to be on the committee?

Answer 1

To find the probability no women are chosen to be on the committee, we need to consider the total number of possible outcomes and the number of outcomes where no women are chosen. The probability no women are chosen is 1/5 or 0.2.

Step-by-step explanation:

To find the probability no women are chosen to be on the committee, we need to consider the total number of possible outcomes and the number of outcomes where no women are chosen.

There are a total of 6 members nominated, and we need to choose 2 members for the committee. The total number of possible outcomes is given by the combination formula C(6,2), which is equal to 15.

Now, let's consider the number of outcomes where no women are chosen. Since all 3 women are nominated, we cannot choose any of them. Therefore, we need to choose 2 members out of the 3 men. The number of outcomes where no women are chosen is given by the combination formula C(3,2), which is equal to 3.

Therefore, the probability no women are chosen to be on the committee is 3/15, which simplifies to 1/5 or 0.2.

Answer 2

Answer: The probability that no women are chosen to be in the committee is 2/5 or 0.40.

Step-by-step explanation:

We have two positions, and we have 6 options for those positions, 3 are men, and 3 are women.

If we want to see the probability where no women are chosen, then this means that in the first selection a man is chosen.

If all the 6 nominees have the same probability of being chosen, then the probability that in the first selection a man is chosen is equal to the number of men divided the total number of nominees, this is:

p1 = 3/6 = 1/2.

Now the same happens for the second selection, but now we have 5 total nominees and 2 are men, so the probability now is:

p2 = 2/5

And the joint probability will be the product of the individual probabilities, then we have:

P = p1*p2 = (1/2)*(2/5) = 2/5.

The probability that no women are chosen to be in the committee is 2/5 or 0.40.