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 $0.008$.
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