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# Probability Question

I roll a die 100 times.  What is the probability that a 3 will appear exactly 35 times?

What is the equation for this?
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Ray Turner
3 Solutions

Commented:
Look at the General Equation here:

http://en.wikipedia.org/wiki/Binomial_probability

The probability of getting exactly 35 threes in 100 rolls .....
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Commented:
Do this:

You need to work out the probability of rolling a three 35 times in one way in a 100 rolls, and then find the probability of these 35 threes being distributed anywhere amongst the 100 rolls.

For the first part you might as well assume the first 35 rolls give a three and the remainder not a three.

for the second part multiply the result from the first part by the nCr of (100 35).

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Senior ConsultantAuthor Commented:
What would the equation look like for this problem?
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Commented:
(1/6)^35 * (1-(1/6))^(100-35) * C(100,35)
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Commented:
d-glitch's link describes exactly what formula you need, take a look at the examples.
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Commented:
Just formating @ozo's response:

Here is the general equation (from Wikipedia):
43a8bb344da218d6f0218e8310339250.png
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Senior ConsultantAuthor Commented:
Thanks!
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