Question

Mr. Hauseman has 17 students in his class, three of whom are freshmen, and the rest are from other classes. He is going to draw two students randomly to be partners.

He calculates the probability of drawing a freshman and then a junior to be
9/136. How many juniors must be in the class?
a.3 b.6 c.7 d.8

Answer 1

b.6

Explanation:

Answer 2

6

Explanation:

Total students = 17

No. of freshmen = 3

Let number of juniors be x.

Since we are given that two students are drawn randomly .

He calculates the probability of drawing a freshman and then a junior to be
`(9)/(136)`

So, probability of getting freshman on first draw =
`(3)/(17)`

Since 1 student is already drawn .So, total no. of students = 16

So, probability of getting Junior on second draw =
`(x)/(16)`

So, probability of getting freshman and junior =
`(3)/(17) * \frac{x}[16}`

Since we are given that the probability of drawing a freshman and then a junior to be
`(9)/(136)`

So,
`(9)/(136)=(3)/(17) * \frac{x}[16}`

`(9)/(136)=(3x)/(272)`

`(9 * 272)/(136 * 3)=x`

`6=x`

Hence there must be 6 juniors in the class.