SOLUTION: A pair of dice is rolled seven times. Find the probability of rolling an even total exactly once. The probability that an even total is rolled exactly once is
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Question 990557: A pair of dice is rolled seven times. Find the probability of rolling an even total exactly once. The probability that an even total is rolled exactly once is
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
There is 1 way to make a 2, 3 ways to make four, 5 ways to make six, 5 ways to make 8, 3 ways to make ten, and 1 way to make 12, for a total of 18 ways to make an even number.
There are 2 ways to make three, 4 ways to make five, 6 ways to make seven, 4 ways to make nine, and 2 ways to make eleven, for a total of 18 ways to make an odd number.
Hence, the probability of an even total on any given roll is 
The probability of 
successes in 
trials where 
is the probability of success on any given trial is given by:
\ =\ {{n}\choose{k}}\left(p\right)^k\left(1\,-\,p\right)^{n\,-\,k})
Where 
is the number of combinations of things taken at a time and is calculated by !})
You need the probability of 1 success in 7 trials where the probability of success on any given trial is 0.5, so:
\ =\ {{7}\choose{1}}\left(0.5\right)^1\left(1\,-\,0.5\right)^{7\,-\,1})
Get out your calculator.
John
My calculator said it, I believe it, that settles it
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