Answer to Question #253124 in Statistics and Probability for Matt

Question

Three dice are rolled together. What is the probability as getting at least one '4'

Answer 1

total number of ways:

$n=6^3=216$

number of ways to get one '4':

$n_1=3\cdot6^2=108$

number of ways to get two '4':

$n_2=3\cdot6=18$

number of ways to get three '4':

$n_3=1$

the probability of getting at least one '4'

$p=\frac{n_1+n_2+n_2}{n}=\frac{108+18+1}{216}=\frac{127}{216}$