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?

Given:

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

To do:

We have to find the probability that the 2 students have the same birthday.

Solution:

Let the probability of 2 students having the same birthday be $p(A)$ and the probability of 2 students not having the same birthday be $p(\overline{A})$.

This implies,

$p(\overline{A})=0.992$

We know that,

$p(E)+p(\overline{E})=1$

Therefore,

$p(A)+0.992=1$

$p(A)=1-0.992=0.008$

The probability that the 2 students have the same birthday is $0.008$.