Question

In university admitted 100 students who transferred from other institutions. Of these students, 34 transferred from two-year community colleges, 25 transferred from private four-year institutions, and the rest transferred from public four-year institutions. If two different students are to be selected at random from the 100 students, what is the probability that both students selected will be students who transferred from two-year community colleges?

Give your answer as a fraction.

• A. $\frac{17}{50}$
• B. $\frac{17}{150}$
• C. $\frac{13}{50}$
• D. $\frac{11}{50}$

Answer 1

The correct option is B $\frac{17}{150}$

Given,

No. of students transferred from 2-yr. community college $=34$

Probability of selecting 1st student ,

$P\left(A\right)=\frac{34}{100}=\frac{17}{50}$

Probability of selecting 2nd student,

$P\left(B\right)=\frac{34-1}{100-1}=\frac{33}{99}=\frac{1}{3}$

Hence, the probability of selecting both the students from 2-yr. community college will be

$=P\left(A\right)P\left(B\right)$

$=\frac{17}{50}\times \frac{1}{3}=\frac{17}{150}$