Asked by Curtis
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)?
Answers
Answered by
Reiny
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
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
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