Question

In a class of $70$ students there are $40$ boys and $30$ girls. $20$ percent of boys and $30$ percent of girls have grey hair and remaining have black hair. A student is selected at random from the class. Let $A,B$ denote the event that the selected student has grey hair, black hair repectively and $E,F$ denote the event that the selected student is boy, girl repectively, then $P(B\cap F)=$

• A. $\frac{8}{17}$
• B. $\frac{3}{10}$
• C. $\frac{3}{7}$
• D. $\frac{7}{10}$

Answer 1

The correct option is B $\frac{3}{10}$

$P\left(E\right)=\frac{40}{70},P\left(F\right)=\frac{30}{70}$
$P\left(\frac{B}{F}\right)=$ probablity of selecting a student having black hair and she is a girl.
$P\left(\frac{B}{F}\right)=\frac{70}{100}$
We know, $P(B\cap F)=P\left(F\right).P\left(B/F\right)=\frac{30}{70}\times \frac{70}{100}=\frac{3}{10}$