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Progressive probability (Posted on 2016-06-15) Difficulty: 4 of 5
Roll a ten-sided die. You succeed if you roll a 1.
Otherwise roll again, this time you succeed if you roll a 1 or a 2.
Otherwise roll again, this time you succeed if you roll a 1, 2 or 3.
Otherwise continue the pattern until you eventually win.

Let x = number of tries to success. What is the expected value of x?

Extend to an n-sided die and give a formula for E(n,x).

For any value of n there is a maximum k such that P(x≤k)≤1/2. Find a formula for this k in terms of n.

This might make an interesting casino game but I've never seen it before.

No Solution Yet Submitted by Jer    
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  Subject Author Date
Some Thoughtscomputer exploration - solution for first part onlyCharlie2016-06-15 15:57:28
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