Find the indicated probability.
-Find the probability that 3 randomly selected people all have the same birthday. Ignore leap years. Round to eight decimal places.
A) 0.00000002
B) 0.00000751
C) 0.3333
D) 0.0082

Question

Quizplus · Accepted Answer

This is a classic example of the birthday problem in probability. The probability that the first person has a unique birthday is 1. The probability that the second person also has a unique birthday is (364/365), since there are 364 possible unique birthdays left out of 365. The probability that the third person also has a unique birthday is (363/365), since there are 363 possible unique birthdays left out of 365. To find the probability that all three have the same birthday, we subtract the total probability of all three having unique birthdays from 1. Therefore, the probability is:
1 - 1 x (364/365) x (363/365) = 0.00000751 (rounded to 8 decimal places). Thus, the best choice is B.

Find the Indicated Probability