Question

Find the probability of getting 5 exactly twice in 7 throws of die.

Answer 1

S={1,2,3,4,5,6}

$\Rightarrow$ n(S)=6

A={S} $\Rightarrow$ n(A)=1

P=$\frac{n(A)}{n(S)}=\frac{1}{6}$ and q=1-p=$1-\frac{1}{6}=\frac{5}{6}$

n=7, r=2 and P(X=r)=$^nC_rp^rq^{n-r}$

P(X=2)

= $^7C_2\bigg(\frac{1}{6}\bigg)^2\bigg(\frac{5}{6}\bigg)^3=\frac{7*6}{1*2}\bigg(\frac{1}{6}\bigg)^7\bigg(5\bigg)^3=\frac{7}{12}\bigg(\frac{5}{6}\bigg)^3$