Question

Electric switches are shipped in packages of 12 items. The probability that an item is defective is 0.15. What is the probability that one package contains: (a) at least one defective switch; (b) more than one defective switch. (c) If the shipper decides to compensate the buyer for the defective switches by paying $2 for each defective switch, what is the expected compensation amount for each package of 12 items?

Answer 1

Binomial distribution: P(X) = nCx p^x q^n-x

Sample size, n = 12

P(an item is defective), p = 0.15

q = 1 - p =0.85

a) P(at least one defective switch) = 1 - P(no defective switch)

= 1 - P(0)

= 1 - 0.85¹²

= 0.8578

b) P(more than one defective switch) = 1 - P(1 or less defective switch)

= 1 - P(0) - P(1)

= 1 - 0.85¹² - 12x0.15x0.85¹¹

= 0.5565

c) Expected number of defective switches = 12x0.15

= 1.8

Expected compensation amount for each package of 12 items = Expected number of defective switches x cost paid for each defective switch

= 1.8 x 2

= 3.6