If you roll four dice, what are the odds of getting three ones?

Question

Using the run-of-the-mill d6, naturally.

Answer 1

(1/6)(1/6)(1/6)(5/6)(4)=20/1296

Answer 2

Binomial distribution:

$n = 4,$ $P(\text{get a 1}) = P(Success) = 1/6.$ If $X =$ the number of 1's in 4 rolls then $$P(X = 3) = {4 \choose 3}(1/6)^3(5/6) = 0.0154.$$

 choose(4,3)*(1/6)^3*(5/6)
 ## 0.0154321
 dbinom(3, 4, 1/6)
 ## 0.0154321

If it's $P(X \ge 3)$ you want, then the answer is $P(X = 3) + P(X = 4) = 0.0162.$

 sum(dbinom(3:4, 4, 1/6))
 ## 0.01620370