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# Probability Question

Posted on 2011-03-09
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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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Question by:Ray Turner
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Assisted Solution

d-glitch earned 332 total points
ID: 35084415
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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Expert Comment

ID: 35084431
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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Author Comment

ID: 35084487
What would the equation look like for this problem?
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Accepted Solution

ozo earned 336 total points
ID: 35084675
(1/6)^35 * (1-(1/6))^(100-35) * C(100,35)
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Expert Comment

ID: 35084705
d-glitch's link describes exactly what formula you need, take a look at the examples.
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Assisted Solution

wdosanjos earned 332 total points
ID: 35084946
Just formating @ozo's response:

Here is the general equation (from Wikipedia):
43a8bb344da218d6f0218e8310339250.png
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Author Closing Comment

ID: 35084970
Thanks!
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