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?

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Solution

Total number of students = 40.
Number of boys = 15.
Number of girls = 25.

(i) Let E₁ be the event of getting a girl's name on the card.

∴ P(selecting the name of a girl) = P(E₁) = $\frac{Number of outcomes favourable to E_{1}}{Number of all possible outcomes}$
= $\frac{25}{40} = \frac{5}{8}$

Thus, the probability that the name written on the card is the name of a girl is $\frac{5}{8}$ .

(ii) Let E₂ be the event of getting a boy's name on the card.

∴ P(selecting the name of a boy) = P(E₂) = $\frac{Number of outcomes favourable to E_{2}}{Number of all possible outcomes}$
= $\frac{15}{40} = \frac{3}{8}$

Thus, the probability that the name written on the card is the name of a boy is $\frac{3}{8}$ .

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