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?

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

Total number of possible outcomes = Total ways to select 2 students from 8 = 8C2 = 28

Number of favorable outcomes = Ways to select 2 females from 3 = 3C2 = 3

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

To find the probability of selecting 2 males, we follow the same steps:

Total number of possible outcomes = Total ways to select 2 students from 8 = 8C2 = 28

Number of favorable outcomes = Ways to select 2 males from 5 = 5C2 = 10

Therefore, the probability of selecting 2 males is 10/28, which simplifies to 5/14.

To find the probability of selecting 2 females, we first need to calculate the total number of possible pairs that can be chosen from the group of 8 students.

The total number of pairs = (Total number of students) choose (Number of students to be selected)
= 8 choose 2
= C(8,2)
= (8!)/((8-2)!*2!)
= (8*7)/(2*1)
= 28

Now, let's find the number of pairs that consist of 2 females. Since there are 3 females in the group, we need to choose 2 from them.

Number of pairs of 2 females = (Number of females) choose (Number of females to be selected)
= 3 choose 2
= C(3,2)
= (3!)/((3-2)!*2!)
= (3*2)/(2*1)
= 3

Therefore, the probability of selecting 2 females is given by:

P(2 females) = (Number of pairs of 2 females) / (Total number of pairs)
= 3/28

To find the probability of selecting 2 males, we use the same approach:

Number of pairs of 2 males = (Number of males) choose (Number of males to be selected)
= 5 choose 2
= C(5,2)
= (5!)/((5-2)!*2!)
= (5*4)/(2*1)
= 10

Therefore, the probability of selecting 2 males is:

P(2 males) = (Number of pairs of 2 males) / (Total number of pairs)
= 10/28

Note: The sum of the probabilities of all possible outcomes must equal 1, so you can also calculate the probability of selecting 2 males by subtracting the probability of selecting 2 females from 1.

P(2 males) = 1 - P(2 females)
= 1 - (3/28)
= 25/28