In a school of 100 children, 50 play cricket and 60 play football. Find the probability that a student selected at random plays both the sports if each of the student plays at least one sport.

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Solution

The correct option is B

Let x be the number of students play both the sports.

Students who play only cricket = 50-x

Students who play only football = 60-x

It is given that a student plays at least one sport

100 = students who play only cricket + students who play only football +students who play both

100 = (50-x) + (60-x) +x $\Rightarrow$ x =10

Probability that a student plays both the sports = $\frac{10}{100}$ = $\frac{1}{10}$

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