Question

The probability of obtaining a double is 1/6 on two fair dice.
Four players play a board game with these two dice.
What's the probability that a double occurs exactly once in 4 of the first 5 rounds?

Answer 1

first selecting 4 rounds out of 5C4=5!/4!
now probability of occurring 4 doubles =1*1*1*1*5/(6*6*6*6*6)
Probability=5c4*5/6^5
25/7776

Answer 2

Thanks for trying so hard, but that's not the answer... I don't know how to get to the answer, but I know what it is, if it may help. The answer is 0.068

Answer 3

\[p={4\choose 1}\frac{1}{6}\left(\frac{5}{6}\right)^3=\frac{125}{324}\]

now do do what ash was doing, but with this value of p

\[{5\choose 4}p^4(1-p)^1=\frac{242919921875}{3570467226624}\approx.068035891791\]