SOLUTION: A pair if dice is rolled four times. Find the probability of rolling an even total exactly once.

Question 1019725: A pair if dice is rolled four times. Find the probability of rolling an even total exactly once.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the probability of getting an even number total on any one roll of the pair of dice is .5

the probability of not getting an even number total on any one roll of the pair of dice is therefore also equal to .5.

p = probability of success = .5
q = probability of failure = 1 - p = .5

the formula for binomial probability is:

p(x) = p^x * q^(n-x) * c(n,x)

in your problem:

x = 1
n = 4
p = .5
q = .5
n-x = 4-1 = 3

p(x) = p^x * q^(n-x) * c(n,x) becomes:

p(1) = .5^1 * .5^3 * c(4,1)

c(4,1) = 4! / (1! * 3!) = (4*3!) / (3!) = 4

this becomes:
p(1) = .5^1 * .5^3 * 4 which becomes:
p(1) = .5 * .125 * 4 which becomes:
p(1) = .25

the probability of rolling an even total exactly 1 time is equal to .25

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