Question 298176: What is the probability of tossing a number cube 12 times and getting exactly six 6's?
My answer key says .0066, but I get a different answer. I thought it would be 1/6 to the power of 6, or 1/3 to the power of 6.
Can you please help?
Thank you very much!!!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! What is the probability of tossing a number cube 12 times and getting exactly six 6's?
My answer key says .0066, but I get a different answer. I thought it would be 1/6 to the power of 6, or 1/3 to the power of 6.
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There are many ways for the six 6's to show up in the 12 tosses.
Each way has probability (1/6)^6(5/6)^6 = 0.000007178....
and there are 12C6 = 924 ways this can happen.
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So the probability of getting exactly six 6's is 924*0.000007178..
= 0.0066
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The formula is 12C6(1/6)^6(5/6)^6
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Cheers,
Stan H.
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