SOLUTION: What is the probability that 19 rolls of a fair die will show 6 fives?

Question 1101120: What is the probability that 19 rolls of a fair die will show 6 fives?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
we use the binomial probability formula
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Probability(P) (k successes in n trials) = nCk * p^k * (1-p)^(n-k), where nCk = n! / (k! * (n-k)!)
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for this problem n=19, k=6, p = 1/6
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Note p = 1/6 is the probability of rolling a 5 with a six sided fair die
:
P ( 6 successes in 19 trials ) = 19C6 * (1/6)^6 * (1-(1/6))^(19-6) = 0.0543 approximately 0.05
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