Question

A class consists of 80 students, 25 of them are girls and 55 boys, 10 of them are rich and the remaining poor, 20 of them are fair complexioned. What is the probability of selecting a fair complexioned rich girl ?

Answer 1

Consider the following events :

A = selecting a fair complexioned student

B = selecting a rich student

C = selecting a girl

We have,

$P\left(A\right)=\frac{20}{80}=\frac{1}{4}$

$P\left(B\right)=\frac{10}{80}=\frac{1}{8}$

$P\left(C\right)=\frac{25}{80}=\frac{5}{16}$

Since, A, B, C are independent events. Therefore,

Required probability = $P(A\cap B\cap C)$

$=P\left(A\right)P\left(B\right)P\left(C\right)=\frac{1}{4}\times \frac{1}{8}\times \frac{5}{16}=\frac{5}{512}$