Question

A class has 8 boys. A pupil is picked at random. The probability of picking a boy is $\frac{1}{5}$. The number of girls in the class who wear glasses is 4. If a pupil is picked at random, find the probability of picking a girl who does not wear galsses.

• A. $\frac{1}{10}$
• B. $\frac{2}{3}$
• C. $\frac{9}{10}$
• D. $\frac{7}{10}$

Answer 1

The correct option is D $\frac{7}{10}$

Total no. of boys in a class $=8$

The probability of picking up a boys is given as $\frac{1}{5}$

$\Rightarrow$ No. of girls in class wearing specs $=4$

$\Rightarrow P($ picking a girl who don't wear glass $)={}^4{C}_4$

$\Rightarrow P($ picking a boys $)={}^8{C}_1$

Probability that a girl does not wear glass $\frac{1}{2}$

$\Rightarrow \frac{{}^8{C}_1-{}^4{C}_4}{5\times 2}=\frac{8-1}{10}=\frac{7}{10}.$

Hence, the answer is $\frac{7}{10}.$