SOLUTION: a die is rolled twenty times.What is the probability of getting exactly four two's?

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Question 574586: a die is rolled twenty times.What is the probability of getting exactly four two's?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Use the binomial probability formula

P(X = x) = (n C x)*(p)^(x)*(1-p)^(n-x)

P(X = 4) = (20 C 4)*(0.1667)^(4)*(1-0.1667)^(20-4)

P(X = 4) = (20 C 4)*(0.1667)^(4)*(0.8333)^(20-4)

P(X = 4) = (4845)*(0.1667)^(4)*(0.8333)^16

P(X = 4) = (4845)*(0.000772)*(0.054053)

P(X = 4) = 0.202177


So the probability of getting exactly four two's is 0.202