A shelf in the Metro Department Store contains 85 colored ink cartridges for a popular ink-jet printer. Six of the cartridges are defective.

Question

(a) If a customer selects 3 cartridges at random from the shelf, what is the probability that they are all defective? (Round your answer to five decimal places.)
 

(b) If a customer selects 3 cartridges at random from the shelf, what is the probability that at least 1 is defective? (Round your answer to three decimal places.)

Answer 1

(a) The probability of the first cartridge being defective is 6/85. There are 84 remaining, and 5 are defective, so the probability of selecting another defective one is 5/84; that leaves 83, 4 defective. The probability of the third being defective is 4/83. The combined probability is 6/85*5/84*4/83=0.00020 approx. (approx 0.02%).

(b) The probability of the first cartridge being OK is 79/85. Now there are 84, including 6 defects, leaving 78. The probability of the second being OK is 78/84 and of the third being OK it's 77/83. The probability of all 3 being OK is therefore 79/85*78/84*77/83=0.800638 approx. Therefore, the probability of at least one being defective is 1-0.800638=0.19936 approx (19.936%), because all other possibilities include at least one defect.