Question

There are $40$ students in a class of whom $25$ are girls and $15$ are boys. The class teacher has to select one student as a class representative. He writes the name of each student on a separate card, the cards being identical. Then she puts cards in a bag and stirs them thoroughly. She then draws one card from the bag. What is the probability that the name written on the card is the name of (i) a girl? (ii) a boy?

Answer 1

Total students $=$ Total outcomes, $n\left(S\right)=40$

Number of girls, $n\left(G\right)=25$

Number of boys, $n\left(B\right)=15$

Probability, $P=\frac{\text{No. of outcomes}}{\text{total no. of outcomes}}$

(i) Probability of getting a girl, $P\left(G\right)=\frac{\text{No. of Girls}}{\text{Total students}}=\frac{n\left(G\right)}{n\left(S\right)}=\frac{25}{40}=\frac{5}{8}$

(ii) Probability of getting a boy, $P\left(B\right)=\frac{\text{No. of Boys}}{\text{Total no. of students}}=\frac{n\left(B\right)}{n\left(S\right)}=\frac{15}{40}=\frac{3}{8}$