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?

Answer 1

Calculate the probability that the students have the same birthday :

Let the event wherein $2$ students don't have the same birthday be $E$

Given, $P\left(E\right)=0.992$

We know that, total probability of an event occurring or not is $1$

So, $P\left(E\right)+P(E\text{'})$ $=1$

Thus, $P(E\text{'})$ $=1–0.992=0.008$

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