What is the probability that at least two(2) of the nine(9) US Supreme Court Justices have the same birth date (month and day)?
The first judge will have a birthday on a certain date
The prob that the second judge will have a different birthday = 364/365
prob that the third judge will have a different b-day than the other two = (364/365)(363/365)
.
prob that the 9th judge will have a different b-day than the other 8 judges
or
all 9 will have a different b-day
= (364/365)(363/365)..(357/365)
so prob that at least 2 will have the same b-day
= 1 - (364/365)(363/365)..(357/365)
= 1-.905376
= .0946