SOLUTION: If 2 fair dice are rolled 15 times, what is the probability that (6,6) will appear only once?

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Question 562461: If 2 fair dice are rolled 15 times, what is the probability that (6,6) will appear only once?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
If 2 fair dice are rolled 15 times, what is the probability that (6,6) will appear only once?
That's a binomial probability problem with n=15 trials.

The probability of a success [rolling (6,6)] is 1%2F36. So we can do it 
by formula:

We want the probability of getting x=1 success out of n=15 trials, where
the probability of 1 success in 1 trial is p=1%2F36, and the
probability of a failure in 1 trial is q = 1-p = 1-1%2F36%29+=+%7B%7B%7B35%2F36  

The binomial probability formula is

C(n,x)pxq(n-x)

C(15,1)%281%2F36%29%5E1%2835%2F36%29%5E%2815-1%29 = 

15%281%2F36%29%2835%2F36%29%5E14 = .2808706559 

You can also do it on a TI-84

Press ON
Press CLEAR
Press 2ND
Press VARS
Press ALPHA
Press MATH

On the newer versions you see this screen.
Type to make it look like this:

trials:15
p:1/36
x value:1
Paste

Use the down arrow key to hilite "Paste"

Press ENTER

You see

binompdf(15,1/36,1)  on the older versions you type to get that.

Press ENTER

Read .2808706559

Edwin