Two men and a woman are lined up to have their picture taken. If they are arranged at random, what is the probability that

(A) the woman will be on the left in the picture?
(B) the woman will be in the middle in the picture?

A and B --- the two men

W ----- the woman

possible cases, there are only 6

ABW
AWB
BAW
BWA
WAB
WBA

I see 2 cases where the woman is on the left
so prob(woman on left ) = 2/6 = 1/3

you do the other case.

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(A) Oh, the woman wants to be in the spotlight, huh? Well, if they are arranged at random, there are three possible positions for the woman: left, middle, and right. Since we know she wants to be on the left, there is only one favorable outcome out of the three possible outcomes.

So, the probability that the woman will be on the left in the picture is 1 out of 3, or 1/3.

(B) Ah, the woman wants to be the center of attention! Well, if they are arranged at random, there are still three possible positions for the woman: left, middle, and right. However, this time she specifically wants to be in the middle.

So, the probability that the woman will be in the middle in the picture is 1 out of 3, or 1/3.

Good luck to her, I hope she gets her desired position!

To find the probability of a specific event occurring, we need to calculate the total number of favorable outcomes (where the event occurs) and divide it by the total number of possible outcomes.

In this scenario, let's assume that the three people are represented as A, B, and C, where A and C are men, and B is a woman.

(A) Probability that the woman will be on the left in the picture:
To calculate this probability, we need to consider that the woman can be placed in any of the three positions (left, middle, or right). However, since we're only interested in her being on the left, there is only one favorable outcome (woman on the left) out of three possible positions.

Total possible outcomes: 3! (3 factorial) = 3 * 2 * 1 = 6
Total favorable outcomes: 1

Therefore, the probability that the woman will be on the left in the picture is 1/6.

(B) Probability that the woman will be in the middle in the picture:
Similarly, for the woman to be in the middle, there is only one favorable outcome, which is the woman being in the middle position.

Total possible outcomes: 3! (3 factorial) = 3 * 2 * 1 = 6
Total favorable outcomes: 1

Hence, the probability that the woman will be in the middle in the picture is also 1/6.