Question

Mr. Hauseman has 17 students in his class, three of which are freshman and the others are sophomores and juniors. He is going to randomly draw two students to be partners. He calculates the probability of drawing first a freshman and THEN a sophomore to be 3 34 . How many sophomores are in the class?

Answer 1

The correct answer would be -8-
I took the test and got it correct!

Answer 2

8

Explanation:

Total number of students = 17

No. of Freshman = 3

Let the number of sophomore be x

Now we are given that He is going to randomly draw two students to be partners.

He calculates the probability of drawing first a freshman and THEN a sophomore to be
`(3)/(34)`

So, probability of drawing a freshman and then a sophomore:

`(^3C_1)/(^(17)C_1)  * (^xC_1)/(^(16)C_1)=(3)/(34)`

`(3)/(17)  * (x)/(16)=(3)/(34)`

`x=(3)/(34) * (17)/(3) * 16`

`x=8`

Hence there are 8 Sophomores in the class.