Question

In a class, there are x girls and y boys, a student is selected at random then the probability of selecting a boy is
(A) \[\dfrac{x}{y}\]
(B) \[\dfrac{x}{x+y}\]
(C) \[\dfrac{y}{x+y}\]
(D) \[\dfrac{y}{x}\]

Answer 1

Hint: The number of boys and girls are \[y\] and \[x\] . Now, calculate the total number of students by adding the number of boys and girls. Use the formula for probability, Probability = \[\dfrac{Number\,of\,favorable\,outcomes}{Total\,number\,of\,favorable\,outcomes}\] . Now, solve it further and calculate the probability of selecting a boy.

Complete answer:
According to the question, we are given that there is a class and there are some boys and girls. We are asked to calculate the probability of selecting a boy.
The number of boys in the class = \[y\] ………………………………….(1)
The number of girls in the class = \[x\] ……………………………………(2)
Since the class has both boys and girls so, the total number of students must be equal to the summation of the number of boys and girls …………………………………(3)
Now, from equation (1), equation (2), and equation (3), we get
The total number of students in the class = \[\left( x+y \right)\] …………………………………….(4)
We know the formula, Probability = \[\dfrac{Number\,of\,favorable\,outcomes}{Total\,number\,of\,favorable\,outcomes}\] ………………………………….(5)
For calculating the probability of selecting one boy, we can use the above formula, i.e.,
Probability of selecting a boy = \[\dfrac{Number\,of\,boys}{Total\,number\,of\,students}\] …………………………………….(6)
Now, from equation (1), equation (4), and equation (6), we get
Probability of selecting a boy = \[\dfrac{y}{\left( x+y \right)}\] .
Therefore, the probability of selecting one boy is \[\dfrac{y}{\left( x+y \right)}\] .

Hence, the correct option is (C).

Note:
For this type of question where we are asked to calculate the probability, always approach this type of question by using the basic formula for the probability, Probability = \[\dfrac{Number\,of\,favorable\,outcomes}{Total\,number\,of\,favorable\,outcomes}\] .