# Estimate the probability that at least two students in a class of 100 share the same ID number

Seeking help with a probability problem.

Assume grades on an exam are posted according to an ID number corresponding to the last 4-digits of a persons social security number ranging from 0000 to 9999.

Assume that each sequence of 4-digits has the same probability.

Q1: Estimate the probability that at least two students in a class of 100 share the same ID number?

So far...

• Class of 100 people
• Each person has an ID number concluding in a sequence of 4-digits.
• There are 10 possibilities {0,1,...,9} for each digit - 1st, 2nd, 3rd, and 4th.
• There are 10^4 total possible outcomes?
• Solution will involve the complement

Any ideas on how to approach this?

• Search our site for the Birthday Problem. A general formula is given at stats.stackexchange.com/questions/57347.
– whuber
Sep 3 '18 at 17:42
• thanks @whuber we have not begun working with the binomial coefficient formula yet but I can see how it is useful for this problems and other variants of the birthday problem. Sep 3 '18 at 22:22