Question

Find the probability of throwing at most 2 sixes in 6 throws of a single die.

Answer 1

The repeated throws of a die are Bernoulli trials.
Let X denotes the number of sixes in 6 throws ofdie.
Obviously, X has the binomial distribution with n = 6

and p =1/6, q=1-1/6=5/6

where p is probability of getting a six
and q is probability of not getting a six
Now, Probability of getting at most 2 sixes in 6 throws = P (X = 0) + P (X = 1) + P (X = 2)