A group of students who are selecting 2 of their group at random to give a report, but assume that there are 5 males and 3 females.

What is the probability that 2 females are selected? 2 males?

There is no replacement. The probability of all/both events is found by multiplying the probabilities of the individual events.

1. 3/8 * 2/7 = ?

2. 5/8 * 4/7 = ?

To find the probability of selecting 2 females, we need to first calculate the total number of possible outcomes and the number of favorable outcomes.

Total number of possible outcomes = total number of ways to select 2 students out of 8 = "8 choose 2" = 8! / (2! * (8-2)!) = 28

Number of favorable outcomes = number of ways to select 2 females out of 3 = "3 choose 2" = 3! / (2! * (3-2)!) = 3

So, the probability of selecting 2 females is 3/28.

Now, let's find the probability of selecting 2 males.

Total number of possible outcomes = 28 (same as before)

Number of favorable outcomes = number of ways to select 2 males out of 5 = "5 choose 2" = 5! / (2! * (5-2)!) = 10

So, the probability of selecting 2 males is 10/28, which can be simplified to 5/14.

Therefore, the probability of selecting 2 females is 3/28, and the probability of selecting 2 males is 5/14.