# 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?

## 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.

**Rasoning:**

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 \(0.008\)