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

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?

Solution:

Given: Probability that 2 students should not have the same birthday

TO FIND: Probability that 2 students should have the same birthday

CALCULATION: We know that sum of probability of occurrence of an event and probability of non occurrence of an event is 1.

$P(E)+P(\bar{E})=1$

$0.992+P(\bar{E})=1$

$P(\bar{E})=1-0.992$

$P(\bar{E})=0.008$

Hence the probability that should have the same birthday is $P(\bar{E})=0.008$