Question

What is the probability that at least two of the nine justices of the U.S. Supreme Court have the same birthday? (Use a 365-day year. Round your answer to four decimal places.)

Answer 1

To calculate the probability that at least two of the nine justices of the U.S. Supreme Court have the same birthday, we can use the concept of complementary probability.

Step-by-step explanation:

To calculate the probability that at least two of the nine justices of the U.S. Supreme Court have the same birthday, we can use the concept of complementary probability.

First, let's calculate the probability that all nine justices have different birthdays. The first justice can have any birthday (365/365), the second justice can have any of the remaining 364 available birthdays (364/365), the third justice can have any of the remaining 363 available birthdays (363/365), and so on.

The probability of all nine justices having different birthdays is calculated as:

P(all different) = (365/365) * (364/365) * (363/365) * ... * ((365 - 8)/365)

Now, we can calculate the probability that at least two justices have the same birthday by subtracting the probability of all nine justices having different birthdays from 1:

P(at least two same) = 1 - P(all different)

Plugging in the numbers:

P(at least two same) = 1 - ((365/365) * (364/365) * (363/365) * ... * ((365 - 8)/365))

Using a calculator or computer software, we can evaluate this expression to find the probability that at least two of the nine justices have the same birthday.