Question

35 boys and 25 girls study in a class. One of the students is selected at random to be the monitor of the class. Find the probability that a girl is selected as the monitor.

Answer 1

Hint: To solve this question, first of all, we need to find a sample set with the chances of anyone being a monitor out of the total students. Thus, we will also need to find the total number of students in the class. Then, we need to find an event set such that only a girl can be the monitor and then we will find the number of elements in that event set. At last, we will find the probability given of event an event occurring is given by the relation $P\left( A \right)=\dfrac{n\left( A \right)}{n\left( S \right)}$, where n(A) is the number of elements in event set A and n(S) is the number of elements in sample event set S.

Complete step-by-step answer:
It is given that there are 35 boys and 25 girls studying in a class.
Let S be the sample event set of selecting any students at random from the class.
The number of elements in sample event set S will be equal to the number of students in the class, as selection is random and unbiased.
Number of students in the class will be equal to the summation of the number of boys and the number of girls.
Therefore, number of students in the class = 35 + 25 = 60
Thus, the number of elements in sample event set S is n(S) = 60.
Let A be the event of selecting a girl as the monitor.
Therefore, the number of elements in event set A will be given as the number of girls in the class.
Therefore, the number of elements in event set A = n(A) = 25.
We know that the probability given of event an event occurring is given by the relation$P\left( A \right)=\dfrac{n\left( A \right)}{n\left( S \right)}$, where n(A) is the number of elements in event set A and n(S) is the number of elements in sample event set S.
$\begin{align}
  & \Rightarrow P\left( A \right)=\dfrac{25}{60} \\
 & \Rightarrow P\left( A \right)=\dfrac{5}{12} \\
\end{align}$
Hence, the probability that the selected monitor is a girl is $\dfrac{5}{12}$ .

Note: Another way to find the probability will be to find the probability that no girl is selected as the monitor. Then we can subtract this probability by unity to find the probability that a girl is the monitor.