Question

In a class, there are 18 girls and 16 boys. The class teacher wants to choose one pupil for the class monitor. What she does, she writes the name of each pupil on a card and puts into a basket and mixes thoroughly. A child is asked to pick one card from the basket. What is the probability that the name written on the card is:
(i) The name of a girl
(ii) The name of a boy

Answer 1

Hint: For solving this question we have to find the probability of the given event for which first we have to find the number of favourable cases for that event and the total number of cases possible. After that, we will solve each part for their correct answer.

Complete step-by-step answer:
Given:
It is given that in a class, there are 18 girls and 16 boys. And to elect the monitor the class teacher writes the name of each pupil on a card and puts into a basket and mixes thoroughly. After that, a child is asked to pick one card from the basket. And we have to find the probability that the name written on the card is of a girl for the first part and the name written on the card is of a boy. For the second part.
Now, in this problem, we have to find the probability of the given event for which first we have to find the number of favourable cases for that event and the total number of cases possible. After calculating both we can find the probability as per the following relation:
$P(E)=\dfrac{F}{T}$ Where,
$P(E)=$Probability of event E.
$F=$The number of favourable cases for the event E.
$T=$Total number of cases possible.
Now, as there are total $18+16=34$ students so, the total number of cards will be 34. Thus, the total number of cases possible will be 34 $\left( T=34 \right)$ . And as it is given that there are 18 girls, the number of cards on which the name of a girl is written will be 18. Thus, the number of favourable cases will be 18 $\left( F=18 \right)$.
Now, for the first part, the probability that the name written on the card is the name of a girl will be equal to $P(E)=\dfrac{F}{T}=\dfrac{18}{34}=\dfrac{9}{17}$ .
Now, as there are total $18+16=34$ students so, the total number of cards will be 34. Thus, the total number of cases possible will be 34 $\left( T=34 \right)$ . And as it is given that there are 16 boys, the number of cards on which the name of a boy is written will be 16. Thus, the number of favourable cases will be 16 $\left( F=16 \right)$.
Now, for the second part, the probability that the name written on the card is the name of a boy will be equal to $P(E)=\dfrac{F}{T}=\dfrac{16}{34}=\dfrac{8}{17}$ .

Note: Here, the student should first try to understand what is asked in the question. After that, we should apply the very basic concept of probability and directly apply the formula. Moreover, though the problem is very easy, we should proceed stepwise and avoid calculation mistakes while solving the question to get the correct answer.