Question

1.     A company manufactures fuses. The percentage of non-defective fuses is 95.4%. A sample of 10 fuse was selected. Calculate the probability of selecting at least 3 defective fuses.     

Answer 1

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

Given $n=10, p=1-0.954=0.046,q=0.954$

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

$$-P(X=2)=1-\dbinom{10}{0}(0.046)^0(0.954)^{10-0}$$

$$-\dbinom{10}{1}(0.046)^1(0.954)^{10-1}$$

$$-\dbinom{10}{2}(0.046)^2(0.954)^{10-2}$$

$$\approx0.0091518085$$