SOLUTION: You toss a fair 6-sided die 5 times. Find the probability that a three is never rolled.
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Question 388086: You toss a fair 6-sided die 5 times. Find the probability that a three is never rolled.
Found 2 solutions by ewatrrr, solver91311:
Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!
Note: The probability of x successes in n trials is:
P = nCx* where p and q are the probabilities of success and failure respectively. In this case p = 1/6 and q = 5/6
nCx =
P(0 successes out of five rolls) = (5/6)^5 = .4019
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The probability of 
successes in 
trials where 
is the probability of success on any given trial is given by:
\ =\ \left(n\cr k\right\)p^k\left(1\,-\,p\right)^{n\,-\,k})
Where )
is the number of combinations of things taken at a time and is calculated by !})
You want 
, 
, and 
, so:
\ =\ \left(5\cr 0\right\)\left(\frac{1}{6}\right)^0\left(\frac{5}{6}\right)^{5})
Note that \ =\ 1\ \forall\ n\ \in\ \mathbb{N})
and 
So the calculation reduces to:
\ =\ \left(\frac{5}{6}\right)^{5})
A little calculator work and you are there.
John
My calculator said it, I believe it, that settles it
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