Question

The United States Department of Agriculture reports that, under its standard inspection system one in every 100 slaughtered chickens passes inspection for faecal contamination. Find the probability that, in a random sample of 6 slaughtered chickens, at least one passes inspection for faecal inspection.

Answer 1

Let $X=$ the number slaughtered chickens passed inspection for faecal contamination: $X\sim Bin (n, p).$

Given $n=6, p=0.01., q=1-p=0.99.$

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

$$=1-\dbinom{6}{0}(0.01)^{0}(0.99)^{6-0}$$

$$=0.058519850599$$