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

We will first find out the total number of students by adding the number of boys and girls. After this, we will find the required probability by putting the values in formula of probability of any event E.

Complete step-by-step answer:
Let us first discuss the formula of the probability of any random event E.
The probability of an event E is given by: $P(E) = \dfrac{{n(F)}}{{n(S)}}$, where n (F) is the number of points in the favourable space and n (S) is the total number of possibilities or the number of points in the sample space.
Here, we are given that a class has 20 girls and 16 boys.
We need to find the probability that if a random student is selected, then it is a girl.
So, let E be the event that the picked student is a girl.
Since, the number of girls in the class are 16.
So, we have n (F) = 16.
Now, the class has a total of 20 + 16 = 36 students.
Therefore, the number of points in sample space is n (S) = 36.
Now, putting these values in the formula, we will then obtain:-
$\Rightarrow P(E) = \dfrac{{20}}{{36}}$
We can simplify and write it as:-
$\Rightarrow P(E) = \dfrac{5}{9}$

Hence, the correct option is (B).

Note:
The students must know that the Sample Space is the set of all possible outcomes of any event E and F is the set of favourable outcomes of any event E.
Now, if you are required to find the probability of getting a boy, you may use the same method or just subtract the possibility of a girl from 1.
The students must also note that “Probability is such an interesting topic that if we use it in our real lives as well, we can find the possibilities of our winnings and losing at any game and so much more”.