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Topic: Dice rolls (Read 1038 times) |
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Altamira_64
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Posts: 116
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Dice rolls
« on: May 31st, 2013, 11:17pm » |
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What is the probability of rolling:
at least one 6 in 6 dice rolls?
at least two 6 in 12 rolls?
at least three 6 in 18 rolls?
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pex
Uberpuzzler
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Posts: 880
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Re: Dice rolls
« Reply #1 on: Jun 1st, 2013, 12:46am » |
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The probability of rolling at least n sixes in 6n rolls is 1 - sum(k=0..n-1) (6n choose k) (1/6)^k (5/6)^(6n-k). So:
for n=1, 1 - (5/6)^6 = 0.665
for n=2, 1 - (5/6)^12 - 12*(1/6)*(5/6)^11 = 0.619
for n=3, 1 - (5/6)^18 - 18*(1/6)*(5/6)^17 - (18*17/2)*(1/6)^2*(5/6)^16 = 0.597
As n goes to infinity, a Central Limit Theorem can be applied to show that the probability approaches 0.5.
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