Answer to Question #283054 in Statistics and Probability for Jyoti

Question

A sample 10 pieces was examined out of a large consignment which has 5% defective pieces .Give the probability of 1 defective in the sample of 10.

Answer 1

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

Given $n=10, p=0.05.$

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

$$\approx0.315125$$

The probability of 1 defective in the sample of 10 is 0.315125.