Question

Mr. Stenfanski's class has 7 boys and 10 girls. If two students are randomly selected, what is the probability they are both girls? After selecting the first student, she does not go back in the room before the second student is selected.

A. 10/17
B. 59/143
C. 10/7
D. 45/136​

Answer 1

`(45)/(136)`

Explanation:

The probability of selecting a girl on the first pick is 10/17, since there are 10 girls out of 17 students in total.

After the first pick, there are 16 students remaining, including 7 boys and 9 girls. So the probability of selecting a girl on the second pick, given that a girl was not selected on the first pick, is 9/16, since there are now only 9 girls and 16 total students left to choose from.

To find the probability of both events occurring (i.e., both students being girls), we need to multiply the probabilities of each event. Therefore, the probability of selecting two girls in a row is:

`(10)/(17) * (9)/(16) = (90)/(272)`

So the probability of selecting two girls in a row is

`(90)/(272)`

which can be simplified to

`(45)/(136)`