SOLUTION: If a fair die is rolled 7 times, what is the probability, to the nearest thousandth, of getting exactly 3 twos?

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Question 1156338: If a fair die is rolled 7 times, what is the probability, to the nearest thousandth, of getting exactly 3 twos?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


P(two) on each roll is 1/6; P(other) on each roll is 5/6.

The number of ways to select 3 of the 7 rolls to be the twos is C(7,3)

P(3 twos in 7 rolls) = %28C%287%2C3%29%29%28%281%2F6%29%5E3%29%28%285%2F6%29%5E4%29

Use a calculator and round as directed.

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.

P = C%5B7%5D%5E3%2A%281%2F6%29%5E3%2A%285%2F6%29%5E4 = %28%287%2A6%2A5%29%2F%281%2A2%2A3%29%29%2A%281%2F6%29%5E3%2A%285%2F6%29%5E4 = 0.078143 = 0.078 (rounded).     ANSWER


It is the binomial type probability distribution.


The number of trial n= 7; the probability of the success trial is  1%2F6,  and the number of success trial k = 3.