SOLUTION: I need to find the classic probability of rolling a 1 (or any number) out of 8 dice. I'm not looking for the total face value, just the frequency of rolling a 1 out of 8 dice. So,

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Question 89327: I need to find the classic probability of rolling a 1 (or any number) out of 8 dice. I'm not looking for the total face value, just the frequency of rolling a 1 out of 8 dice. So, "What is the probability that you will roll a single 1 out of 8 dice?", "What is the probability you will roll two 1s out of 8 dice?" and so on.
What I have tried:
(when rolling no 1s out of 8 dice) I used:
(when rolling a single 1 out of 8 dice) I used: .
(when rolling two 1s out of 8 dice) I used:
Alternately, I tried the same thing without using powers in my formulas.... but this didn't seem to help.
My total probability for the set did not add up to 1, so I think I must be missing a step? Please help!
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Your numbers have taken care of the independent nature of the event but
not the mutually exclusive nature of the event.
For example getting one "1" on the 8 dice is (1/6)^1(5/6)^7 takes care
of getting the "1" on the 1st dice; but getting the one on the
2nd dice is a mututally exclusive event and has the same probability,
and the same for a "1" on the 3rd dice etc.
So the probability of getting one "1" is 8C1(1/6)(5/6)^7 = 8(1/6)(5/6)^7
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Similarly the probability of getting two "1's" is 8C2(1/6)^2(5/6)^6=
28(1/6)^2(5/6)^6
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If you continue this to 8C8(1/6)^8(5/6)^0 and add up the terms they will
add up to one.
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Cheers,
Stan H.