Homework SourseA shelf in the Metro Department Store contains 80 colored in
A shelf in the Metro Department Store contains 80 colored ink cartridges for a popular ink-jet printer. Eight of the cartridges are defective.
(a) If a customer selects 2 cartridges at random from the shelf, what is the probability that both are defective? (Round your answer to five decimal places.)
(b) If a customer selects 2 cartridges at random from the shelf, what is the probability that at least 1 is defective? (Round your answer to three decimal places.)
Solution
(a) There are 80 colored ink cartridges of which 8 are defective. The probability of the 1st cartridge picked up by the customer being defective is 8/80. There are now 79 cartridges left of which 7 are defective. The probability of the 2nd picked up by the customer being defective is 7/79. The probability that both the cartridges picked up by the customer being defective is (8/80) * (7/79) = 56/ 6320 =0.0088607594 = 0.00886 ( on being rounded off to 5 decimal places)
(b) To determine the probability of at least one cartridge being defective, let us compute first the probability of none of the 2 cartridges being defective. There are 80 cartridges of which 72 are good so that the probability of the 1st cartridge not being defective is 72/80. Having selected 1 good cartridge , there are 79 cartridges left, of which 71 are good so that the probability of the 2nd cartridge being defect free is 71/79. Thus, the probability of both the cartridges being defect free is (72/80)* (71/79) = 5112/ 6320 = 0.808860759. Now, the probability that at least 1 cartridge is defective is 1 - 0.808860759 = 0.19113924= 0.191 ( on being rounded off to 3 decimal places)
