Math Help - Dice Probability

1. Dice Probability

Question: A dice is rolled six times. Find the probability that a three is rolled exactly twice.

My thoughts: I thought i could do (1/6)(1/6)(5/6)(5/6)(5/6)(5/6), because (1/6)(1/6) accounts for the two three's, and the (5/6)(5/6)(5/6)(5/6) accounts for the other four rolls, being anything but a three. Apparently this is wrong, because i get: 625/46656, and the correct answer is: 3125/15552.

Any suggestions? help is appreciated.

2. Use Binomial Distribution.

n = 6

x=2

p=1/6

3. i'm sorry, but your explanation is extremely vague. Can you expand on what you are trying to say?

4. I guess you have very less idea about what BINOMIAL DISTRIBUTION is. Have a look at the link..

The probability mass function of a Binomial distribution is:

$P(X=x) = \dbinom{n}{x} \; p^x \; (1-p)^{n-x}$

The values of n, p, x are given in Post # 2. Find the required probability.

Is this clear?