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 write the name of each student on a separate. the card being is the probability that the name written on the card is the name of

(i) A girl ?

(ii) A boy ?

Answer 1

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 of the cards

Therefore, P(selecting the name of a girl) = P(E₁) = \(\cfrac{number\,of\,outcomes\,favorable\,to\,E_1}{number\,of\,all\,possible\,outcomes}\) = \(\frac{25}{40}\) = \(\frac{5}{8}\)

Thus, the probability that the name written on the card is the name of a girls is \(\frac{5}{8}\).

(ii) Let E₂ be the event of getting a boy's name of the cards

Therefore, P(selecting the name of a boy) = P(E₂) = \(\cfrac{number\,of\,outcomes\,favorable\,to\,E_2}{number\,of\,all\,possible\,outcomes}\) = \(\frac{15}{40}\) = \(\frac{3}{8}\)

Thus, the probability that the name written on the card is the name of a boys is \(\frac{3}{8}\).