SOLUTION: A die is tossed 12 times. What is the probability of getting exactly three 3's?

Question 866650: A die is tossed 12 times. What is the probability of getting exactly three 3's?
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A die is tossed 12 times. What is the probability of getting exactly three 3's?
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Binomial Problem with n = 12 and P(3) = 1/6
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P(x = 3) = 12C3(1/6)^3*(5/6)^9 = binompdf(12,1/6,3) = 0.1974
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Cheers,
Stan H.
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Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
This is a binomial distribution problem with p = 1/6 (that's the probability of rolling a single 3), n = 12

In this case, x = 3 since we want exactly 3 threes.

Now compute n C x = 12 C 3 = (12!)/(3!*(12-3)!) = 220. This is the binomial coefficient.

So we'll then have 220*p^(x)*(1-p)^(n-x) = 220*(1/6)^(3)*(1-1/6)^(12-3) = 0.19739571242092

So the probability of getting exactly 3 threes is approximately 0.19739571242092 (roughly 19.73957%)
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