Question

In a certain college, 25% of boys and 10% of girls are studying mathematics. The girls constitute 60% of the student body. If a student is selected at random from student body and is found to be studying mathematics, then the probability that the student is a girl is______.

• A. 0.375

Answer 1

The correct option is A 0.375
$P\left(Girl\right)=P\left(G\right)=\frac{60}{100}=\frac{3}{5}$

$P\left(Boy\right)=P\left(B\right)=\frac{40}{100}=\frac{2}{5}$


Probability that mathematics is studied given that the student is a girl
$=P\left(\frac{M}{G}\right)=\frac{10}{100}=\frac{1}{10}$

By Baye's theorem, probability of maths student is a girl

$=P\left(\frac{G}{M}\right)=\frac{P\left(G\right)P\left(\frac{M}{G}\right)}{P\left(M\right)}=\frac{P\left(G\right)P\left(\frac{M}{G}\right)}{P\left(G\right)P\left(\frac{M}{G}\right)+P\left(B\right)P\left(\frac{M}{B}\right)}$

$=\frac{\frac{3}{5}\times \frac{1}{10}}{\frac{4}{25}}=\frac{3}{8}=0.375$