Answer
a) $p(X=0)\approx 0.86$
b) $p(X\leq 1)\approx 0.99$
c) $p(X\geq 8)\approx 0$
Work Step by Step
Let X be the random variable of the number of mutated samples. then X is distributed as binomial distribution with n=15, p=0.01, this means that
$p(X=x)=\frac{15!}{x!(15-x)!}(0.01)^{x}(0.99)^{15-x}, x=0,1,...,15$
a) $p(X=0)=\frac{15!}{0!(15)!}(0.01)^{0}(0.99)^{15}\approx 0.86$
b) $p(X\leq 1)=p(X=0)+p(X=1)=\frac{15!}{0!(15)!}(0.01)^{0}(0.99)^{15}+\frac{15!}{1!(14)!}(0.01)^{1}(0.99)^{14}\approx 0.99$
c) $p(X\geq 8)=1-p(X\leq 7)\approx 0$ (we can get $p(X\leq 7)$ from the appendix table)
