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
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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):
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
