Question

Suppose three fair dice are rolled. what is the probability that at most one six appears?

Answer 1

The probability of no six appearing is:
$(\frac{5}{6})^{3}=0.5787$
The probability of exactly one six appearing is:
$3C1\times\frac{1}{6}\times(\frac{5}{6})^{2}=0.347$
The events 'no six' and 'one six' are mutually exclusive, therefore the probability of no more than one six is given by:
0.5787 + 0.347 = 0.9257