Question

"jimi has 5000 songs on his ipod shuffle, which picks songs uniformly at" random. jimi plans to listen to 100 songs today. what is the chance he will hear at least one song more than once?

Answer 1

about 63.1%

Explanation:

For the first song, it is certain it isn't a duplicate. For the second song, the probability that it is not a duplicate is 4999/5000. The probability the third song is not a duplicate is 4998/5000.

Hence the probability that none of the 100 songs is a duplicate is ...

5000!/4900!/5000^100 ≈ 0.369120

Then the probability that one or more is a duplicate is ...

1 - 0.369120 ≈ 0.630880