SOLUTION: What is the probability that 6 rolls of a fair die will show four exactly 5 times?

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Question 1041019: What is the probability that 6 rolls of a fair die will show four exactly 5 times?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
You can see this is very very unlikely.

If an event is repeated n times with a probability of success 
each time is p, then the probability of getting exactly x 
successes is given by the binomial formula:

%28nCx%29p%5Ex%2A%281-p%29%5E%28n-x%29

You case is n=6 trials (rolls)
The probability of a success (four) each time is p=1/6  
The number of successes x=5

%286C5%29%281%2F6%29%5E5%2A%281-1%2F6%29%5E%286-5%29

%286%29%281%2F6%5E5%29%2A%285%2F6%29%5E%281%29

%286%29%281%2F7776%29%2A%285%2F6%29


%28cross%286%29%29%281%2F7776%29%2A%285%2Fcross%286%29%29

5%2F7776

Edwin