# Math Help - Dice Probability

1. ## Dice Probability

A dice has 6 faces numbered 1-6. If I roll it 9 times what is the probability that I will get the number 4 exactly 6 times? Answer as a decimal accurate to at least 4 significant figures.

2. Originally Posted by mr_motivator
A dice has 6 faces numbered 1-6. If I roll it 9 times what is the probability that I will get the number 4 exactly 6 times? Answer as a decimal accurate to at least 4 significant figures.
The singular of dice is a die. So a die is rolled nine times.
The probability of getting a 4 on any roll is $\frac {1}{6}$.
In nine rolls there are $9 \choose 6$ ways to get exactly six 4’s in six.
${9 \choose 6}\left( {\frac{1}{6}} \right)^6 \left( {\frac{5}{6}} \right)^3$

3. Binomial distribution with n=9 and p=1/6.
$P(X=x)={9 \choose x}(1/6)^x(5/6)^{9-x}$
where x=0,1,...,9. Where you want x=6.