SOLUTION: What is the probability that at least three of the nine justices of the U.S. Supreme Court have the same birthday? Round your answer to the nearest ten thousandth. ​ 0.0205

First we calculate the number of ways all 9 will have different
birthdays:

So we think of assigning 9 different birth dates from the 365 (ignoring 
Feb. 29, which won't affect the answer much) to the 9 justices:

That's 

Divide that by the number of ways they can have any birthdays, which 
is:




 
We can do that with a calculator by considering it as the product of
fractions:



That comes out to 0.9053761661

That's the probability that they will all have different birthdays.

-----------------------

Next we find the probability that exactly 2 will have the same birthday.

We can choose the 2 to have the same birthday in 9C2 = 36 ways.
We can choose their common birthday in 365 ways.
We can assign different birthdays to each of the other 7 in 364P7 ways.
That's  ways.

So that's 



Divide that by the number of ways they can have any birthdays, which 
is:





We can do that with a calculator by considering it as the product of
fractions:



That comes out to be 0.0912984369

That's the probability that exactly 2 of them will have different birthdays.

------------------------------------------------------

Therefore the probability that NO 3 will have the same birthday is the
sum of those probabilities:

0.9053761661 + 0.0912984369 = 0.9966746030

-----------------------------------------

To find the final answer, we subtract that from 1

0.003325397

Rounding to the nearest ten thousandth:

0.0033.

Edwin