Question

Probability of selecting a boy in a class is $0.6$ and there are $45$ students in the class. Find the number of girls in the class.
A) $16$
B) $15$
C) $18$
D) $14$

Answer 1

Hint:
We will use the definition of probability and establish a relation between the number of boys in the class with the given probability. Using the given number of girls, we will find the general equation for the boys and girls. Then we will write the general equation and solve it for the number of boys.

Complete step by step solution:
It is given that the probability of selecting a boy from a class is $0.6$ .
Let us assume that the total number of boys in the class is $x$ .
It is known that the total number of students in the class is $45$ .
Therefore, the number of girls in the class is $45 - x$ .
Now probability is defined as the ratio of the number of selected events to the number of objects in the sample space.
Using the definition of the probability we can write the following:
$\dfrac{x}{{45}} = \dfrac{6}{{10}}$
Rearrange the equation for $x$ and write the following:
$x = \dfrac{{45 \times 6}}{{10}}$
Therefore, on simplifying for $x$ we write $x = 27$.
From the total number of students, we get, number of girls is $45 - 27 = 18$ .
Therefore, there are $18$ girls in the class.

Thus, option C is the correct option.

Note:
All the required information is already given in the problem, just you need to interpret the information correctly. The number of total students is given and the percentage of boys is given in terms of the probability. We will use it to express the number of boys in terms of the given terms.