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