SOLUTION: Pease help me again: A die is rolled 3 times. What is the probability of? a. no three turning up? b. 1 three? c. 3 three? Thanks again..

Question 1061544: Pease help me again: A die is rolled 3 times. What is the probability of?
a. no three turning up?
b. 1 three?
c. 3 three?
Thanks again..
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
You use the binomial probability distribution
:
a) probability(Pr) of rolling a 3 on one roll is 1/6, therefore
Pr ( k = 0 ) = 3C0 * (1/6)^0 * (5/6)^(3-0)
Pr ( k = 0 ) = 1 * 1 * (5/6)^3 = 125/216 = 0.5787
:
b) Pr ( k = 1 ) = 3C1 * (1/6)^1 * (5/6)^(3-1)
Pr ( k = 1 ) = 3 * (1/6) * (25/36) = 0.3472
:
c) Pr ( k = 3 ) = 3C3 * (1/6)^3 * (5/6)^(3-3)
Pr ( k = 3 ) = 1 * (1/6)^3 * 1 = 1/216 = 0.0046
:
Note 3Ck = 3! / (k! * (3-k)!
:

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