Question

From a class of $12$ girls and $18$ boys, two students are chosen randomly. What is the probability that both of them are girls.

• A. $\frac{22}{145}$
• B. $\frac{13}{15}$
• C. $\frac{1}{18}$
• D. $\frac{1}{15}$

Answer 1

Answer: (A)

$\frac{22}{145}$

Number of ways of selecting 2 students from 30 students = 30C2 ways

= ( 30 x 29 )/2

= 15 x 29 ways

Number of ways of selecting 2 girls from 12 girls = 12C2 ways

= 12 x 11 / 2

= 6 x 11

Thus, probability that both selected students are girls

= ( 6 x 11 ) / ( 15 x 29 )

= 22 / 145