# Ex.15.1 Q7 Probability Solution - NCERT Maths Class 10

## Question

It is given that in a group of $$3$$ students, the probability of $$2$$ students not having the same birthday is $$0.992.$$ What is the probability that the $$2$$ students have the same birthday?

Video Solution
Probability
Ex 15.1 | Question 7

## Text Solution

What is known?

It is given that in a group of $$3$$ students, the probability of $$2$$  students not having the same birthday is $$0.992.$$

What is unknown?

The probability that the $$2$$ students have the same birthday.

Reasoning

This question is straight forward. We know that the sum of two complementary events are $$P\,(E) + P$$ (not $$E$$$$=1.$$

By putting the given values in the above equation, we can find out the probability of not happening of event.

Steps:

Probability that $$2$$ students not having the same birthday $$P$$ (not $$E$$$$= 0.992$$

Probability that $$2$$ students having the same birthday

\begin{align}P(E)&=1-0.992 \\& =0.008 \\\end{align}

Thus, the probability that the $$2$$ students have the same birthday is $$0.008$$

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