Photography - 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?
1 woman, three possible positions.
the Pr of the woman in any position is 1/3
so I don't have to do any Permutations right? just a simple Pr(E)=n(E)/n(S)
If you want to do it that way, go ahead:
you will get the same answer: one thing, three possible positions.
thanks =)
To find the probability in both cases, we need to consider the total number of possible arrangements and the number of favorable arrangements where the woman is in the specified position.
Let's assume that the two men and the woman are distinguishable, meaning that each person has unique characteristics such as different heights or appearances. We also assume that the order from left to right matters in the picture.
(A) Probability that the woman will be on the left in the picture:
To solve this, we need to count the number of favorable arrangements where the woman is on the left and divide it by the total number of possible arrangements.
Total number of possible arrangements: There are three people, so there are 3! (3 factorial) ways to arrange them, which is equal to 3 x 2 x 1 = 6.
Favorable arrangements: The woman needs to be on the left, and the two men can be arranged in any order. That gives us 2! (2 factorial) ways to arrange the two men. Therefore, the number of favorable arrangements is 2 x 2!, which equals 4.
Probability = Favorable arrangements / Total arrangements = 4 / 6 = 2/3.
So, the probability that the woman will be on the left in the picture is 2/3.
(B) Probability that the woman will be in the middle in the picture:
Again, we need to count the number of favorable arrangements where the woman is in the middle and divide it by the total number of possible arrangements.
Total number of possible arrangements: There are three people, so there are still 3! (3 factorial) ways to arrange them, which is still equal to 6.
Favorable arrangements: The woman needs to be in the middle, and the two men can be arranged in any order. That gives us 2! (2 factorial) ways to arrange the two men. Therefore, the number of favorable arrangements is still 2 x 2!, which equals 4.
Probability = Favorable arrangements / Total arrangements = 4 / 6 = 2/3.
So, the probability that the woman will be in the middle in the picture is also 2/3.