What is the probability that two people in your class (assume a class of 30 students) have the same birthday?
A) 70.6%
B) 73.7%
C) 0.1%
D) 65.2%
E) 29.4%

Question

What is the probability that two people in your class (assume a class of 30 students) have the same birthday? ​
A) 70.6%
B) 73.7%
C) 0.1%
D) 65.2%
E) 29.4%

Quizplus · Accepted Answer

The probability that two people in a class of 30 students have the same birthday is best calculated using the complement principle, which is easier than directly calculating the probability of at least two people sharing a birthday. The complement is the probability that no two people share a birthday. For a class of 30, this is calculated by multiplying the probabilities that each subsequent person has a unique birthday, starting with 365/365 for the first person, 364/365 for the second, and so on down to 336/365 for the 30th person. The product of these probabilities gives the chance that no one shares a birthday, and subtracting this result from 1 gives the probability that at least two people do share a birthday. This calculation results in approximately 70.6%, making option A correct.

What Is the Probability That Two People in Your Class