Question

A class has 20 girls and 16 boys. One student is selected at random. Find the probability that the selected student is a girl.
A. \[\dfrac{1}{4}\]
B. \[\dfrac{5}{9}\]
C. \[\dfrac{3}{4}\]
D. \[\dfrac{4}{9}\]

Answer 1

Hint: In this particular problem find the total number of students and then use the probability formula for finding probability of getting a girl on selection. Formula for probability of getting a favourable outcome is = \[\dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Total number of outcomes}}}}\]

Complete step by step answer:
As we know that the number of boys in a class is 16.
And the number of girls in a class = 20.
So, the total number of students in this class will be = number of boys + number of girls = 16 + 20 = 36.
As we know from the concept of the probability that if there are n balls out of then x are of same type A then the probability of getting a ball of type A on random selection is equal to = \[\dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Total number of outcomes}}}}\]. So, in this example favourable outcome will be ball of type A. So, probability = \[\dfrac{{{\text{Number of balls of type A}}}}{{{\text{Total number of balls}}}} = \dfrac{x}{n}\]
So, now let us come to the question. As we know that we have the probability of getting a girl on random selection. So, the favourable outcome must be a girl.
So, probability that the selected student is girl = \[\dfrac{{{\text{Number of girls}}}}{{{\text{Total number of students in class}}}} = \dfrac{{20}}{{36}} = \dfrac{5}{9}\]
Hence, the correct option will be B.
Note: Whenever we face such type of problems the we had to recall the formula for the probability and then find the number of favourable outcome (here number of girls in class) and total number of outcomes (here total number of students in class) and then put their value in the above stated probability formula to find the required answer. This will be the easiest and efficient way to find the solution of the problem.