Probability with Bernoulli Trials

Question

A fair die is rolled repeatedly and each roll counts as a success if a 6 appears. What is the Probability that exactly three 6's will appear in the first 12 rolls? I believe this problem invilves the Bernoulli Process, but I'm not sure how to find the values amd plug them in correctly. Please advise.

Answer 1

rolls :=$n=12$ hits :=$k=3$ probability for hit :=$p_0=\frac{1}{6}$

Use general formula for Bernoulli Trials

$$P(n,k,p_0)=\frac{n!}{k!(n-k)!}p_0^k(1-p_0)^{n-k}$$

$$P=\frac{12!}{3!9!}(\frac{1}{6})^3(1-\frac{1}{6})^{12-3}$$