Answer to Question #349585 in Statistics and Probability for Tsi

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

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

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

$$=0.058519850599$$