Rhee and Pamela are two of the five members of a band. Every week, the band picks two members at random to play on their own for five minutes. What is the probability that Rhee and Pamela are chosen this week?

If they are independently chosen, pr(R,P)=2/5*1/4=1/10

Ohh ok thank you! God bless you

Wait why times 1/4?

of the first choice, there are either of two of the five (2/5) which are acceptable. Then, of the four remaining, only one is acceptable (1/4). Joint probability is (2/5)(1/4)=2/20=1/10

Ohh ok, thank you!!!

Rhee and Pamela are two of the 5 members of a band. Every week, the band picks two members at random to play on their own for five minutes. What is the probability that Rhee and Pamela are chosen this week?

To find the probability that Rhee and Pamela are chosen this week, we need to calculate the ratio of the number of favorable outcomes (Rhee and Pamela being chosen) to the total number of possible outcomes (any two members being chosen).

Let's first determine the total number of possible outcomes. Since they are choosing two members out of five, we can use the combination formula, which is given by:

C(n, r) = n! / (r! * (n-r)!)

In this case, n = 5 (total number of members) and r = 2 (number of members being chosen). Plugging in these values, we get:

C(5, 2) = 5! / (2! * (5-2)! )
= 120 / (2 * 6)
= 120 / 12
= 10

So, there are a total of 10 possible outcomes.

Now, let's determine the number of favorable outcomes. Since Rhee and Pamela need to be chosen, there is only one way this can happen.

Therefore, the probability that Rhee and Pamela are chosen this week is:

Number of favorable outcomes / Total number of possible outcomes
= 1 / 10
= 1/10

Hence, the probability that Rhee and Pamela are chosen this week is 1/10 or 0.1 (10%).