Step 1 :

13).

Total number of students in best buddies are 60.

Among them 20 students are 12^th graders.

Out of 60 students 2 students are selected randomly.

Step 2 :

a).

Find the probability that the 2 students are from 12^th graders.

Assume that the 2 selections are made with replacement.

Let the two events be .

Probability of selecting first student : .

Probability of selecting second student : .

The two events are independent events then .

Probability of selecting 2 students is

.

Probability of selecting 2 students from 12^th graders with replacement is 0.1111.

Step 3 :

b).

Find the probability that the 2 students are from 12^th graders.

Assume that the 2 selections are made without replacement.

Let the two events be .

Probability of selecting first student : .

Probability of selecting second student : .

The two events are independent events then .

Probability of selecting 2 students is

.

Probability of selecting 2 students from 12^th graders with replacement is 0.1073.

Step 4:

(c)

15 students join best buddies.

Total number of students in best buddies are 60+15 =75.

Find the probability that 15 students are 12^th graders.

Number of ways of selecting 15 students from 20 students is . \ \

Number of ways of selecting 15 students from 75 students is .

probability that 15 students from 60 students who are 12^th graders is \ \