assuming that Huawei produces 5% of their total production of smartphones are defective. If 10 items are to be chosen at random from the production line, what then is the probability that; a. all smartphones are not defective? b. at most 2 of the smartphones are defective? c. at least 3 of the smartphones are defective?

Let $X=$ the number of defective smartphones: $X\sim Bin(n, p).$

Given $n=10, p=0.05, q=0.95.$

a.

$P(X=0)=\dbinom{10}{0}(0.05)^0(0.95)^{10-0}$

$=0.59873693924$

b.

$P(X\le 2)=P(X=0)+P(X=1)+P(X=2)$

$=\dbinom{10}{0}(0.05)^0(0.95)^{10-0}$

$+\dbinom{10}{1}(0.05)^1(0.95)^{10-1}+\dbinom{10}{2}(0.05)^2(0.95)^{10-2}$

$=0.59873693924+0.31512470486$

$+0.07463479852=0.98849644262$

c.

$P(X\ge 3)=1-P(X=0)-P(X=1)$

$-P(X=2)=1-\dbinom{10}{0}(0.05)^0(0.95)^{10-0}$

$-\dbinom{10}{1}(0.05)^1(0.95)^{10-1}-\dbinom{10}{2}(0.05)^2(0.95)^{10-2}$

$=1-0.59873693924-0.31512470486$

$-0.07463479852=0.01150355738$