Question

Note this is a statistics question from algebra 2Let’s say that a piece of dice is rolled seven times use the binomial distribution form to determine the possibility of rolling exactly 5 3’s

Answer 1

For this problem, we use the following formula for binomial distribution:

$P(x=k)=\begin{bmatrix}{n} & {} & {} \\ {k} & {} & {} \\ {} & {} & \end{bmatrix}p^k(1-p)^{n-k}$

Where n is the number of times the piece of dice is rolled and p is the probability of getting a specific number k times, substituting n=7, p=1/7, and k=3 we get:

$\begin{gathered} P(x=3)=\begin{bmatrix}{7} & {} & {} \\ {3} & {} & {} \\ {} & {} & {}\end{bmatrix}(\frac{1}{7})^3(1-\frac{1}{7})^{7-3}=\frac{7!}{(7-3)!3!}(\frac{1}{343})(\frac{1296}{2401}) \\ P(x=3)=0.055 \end{gathered}$

Answer: The probability is 5.5%