Joined: Nov 2, 2009
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September 17th, 2021 at 9:32:29 AM permalink
How many die are needed so that any given number has a 50-50 chance of appearing?
Each die has a 1/6th chance of landing on a Five. How many are needed to increase the odds of a 5 being rolled to 50-50?
Please show what formula to use so I can reference it in the future.
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Joined: Feb 18, 2015
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September 17th, 2021 at 9:59:29 AM permalink
The general formula for the problem you have described is:

P = 1- (a)^n where

P = probability of what you want to observe
a = the probability of all the other things that can happen on any given dice roll
and n is the number of dice (or number of rolls)

For your specific problem you want

P = 1-(5/6)^n >= 0.5

You want to find the lowest value of n such that P is greater than or equal to 0.5.

When n =4, P= 0.517747., and four dice are your answer.
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