A 100 sided die
Madeleine has a fair 100 sided die, each face numbered with a distinct number from 1 to 100.
She decides to roll it and record the number until she has rolled all the numbers at least once.
What is the expected value for the number of rolls she will need to make?
Please round your answer to the nearest integer.
Other Expected Value Quizzes
Image credit : toyspedia.blogspot.com
The answer is 519.
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1 solution
This is an example of the coupon collector's problem , where the answer is given by:
E ( 1 0 0 ) = 1 0 0 ∗ ( 1 / 1 + 1 / 2 + 1 / 3 + . . . + 1 / 1 0 0 ) ≈ 5 1 9