The probability that a pen drawn at random from a box of pens is defective is $0.5$. If a sample o

Question

The probability that a pen drawn at random from a box of pens is defective is $0.5$. If a sample of $7$ pens is taken, find the probability that it will contain no defective pens; $5$ or $6$ defective pens; less than $3$ defective pens; the most likely number of defective pens in the sample of $7$ pens; the expected number of defective pens in the sample and their standard deviation.

Accepted Answer

(a)(i) $0.00781$; (ii) $0.219$; (iii) $0.227$; (b) $3$ and $4$; (c) $3.5, 1.32$.