What is the probability that at least two of the nine justices of the U.S. Supreme Court have the same birthday? Round your answer to the nearest ten thousandth.
A) 0.0107
B) 0.0511
C) 0.0114
D) 0.043
E) 0.0946
F) 0.0587

Question

What is the probability that at least two of the nine justices of the U.S. Supreme Court have the same birthday? Round your answer to the nearest ten thousandth. ​
A) 0.0107
B) 0.0511
C) 0.0114
D) 0.043
E) 0.0946
F) 0.0587

Quizplus · Accepted Answer

The probability that at least two people share the same birthday in a group of 9 can be calculated using the complement principle. First, calculate the probability that none of them share a birthday, and then subtract that from 1. The probability that the first justice has a unique birthday is 365/365, for the second it's 364/365 (since one day is taken), for the third it's 363/365, and so on until the ninth justice, which is 357/365. Multiplying these probabilities gives the probability that no two justices share a birthday. Subtracting this product from 1 gives the probability that at least two share a birthday. The calculation is 1 - (365/365 * 364/365 * ... * 357/365) ≈ 0.0946 when rounded to the nearest ten thousandth.

What Is the Probability That at Least Two of the Nine