SOLUTION: If there are 20 students in the class, what is the probability that two or more will have the same last 5 digits in their social security numbers (in the same order)? Assume that

Question 701874: If there are 20 students in the class, what is the probability that two or more will have the same last 5 digits in their social security numbers (in the same order)? Assume that all digits 0 to 9 are equally likely, and give your answer to within +/- 0.000001.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The conceptually simple way to do this is to calculate the probability that NONE of the 20 have the same last 5 digits and then subtract from 1. The probability of "at least one" is the complement of "none".

The arithmetic is, on the other hand, god-awful ugly.

00000 to 99999 is 100,000 numbers.

The probability that in a group of 1 persons that the last five will NOT be duplicated is

.

The probability that in a group of 2 people that the last five will NOT be duplicated is

Then for three:

And so on. The entire calculation is

to get the probability that there are no pairs of students with the same last 5, and then subtract from 1 to get the probability that at least two people share the same last 5. Happy calculator button pushing.

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

The Out Campaign: Scarlet Letter of Atheism

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