ProbabilityHelp
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- Jul 5, 2013
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If I roll a presumably fair 16-sided die 10 times, what are the odds that I will roll at least three sevens? In no specific order, just three sevens or more total during the 10 rolls.
In attempting to calculate the problem I tried to use the formula of 1 minus the sum of the probability of getting A) getting exactly 0 sevens, B) getting exactly 1 seven, and C) getting exactly 2 sevens.
This is what that looked like:
A = (1) * (15/16)^10
B = (10) * (1/16)^1 * (15/16)^9
C = [(10*9)/(1*2)] * (1/16)^2 * (15/16)^13
So I added A, B, and C together to get 0.95. Leaving me with a 5% chance to get at least 3 sevens? Am I doing that correctly? Instinctively it seems like 5% is too high to me.
Would greatly appreciate any advice that can be spared for verifying this problem.
In attempting to calculate the problem I tried to use the formula of 1 minus the sum of the probability of getting A) getting exactly 0 sevens, B) getting exactly 1 seven, and C) getting exactly 2 sevens.
This is what that looked like:
A = (1) * (15/16)^10
B = (10) * (1/16)^1 * (15/16)^9
C = [(10*9)/(1*2)] * (1/16)^2 * (15/16)^13
So I added A, B, and C together to get 0.95. Leaving me with a 5% chance to get at least 3 sevens? Am I doing that correctly? Instinctively it seems like 5% is too high to me.
Would greatly appreciate any advice that can be spared for verifying this problem.