Question

A shelf in the Metro Department Store contains 85 colored ink cartridges for a popular ink-jet printer. Six of the cartridges are defective.
(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 that all 3 are defective in a sample of 3 is:
$P(3)=\frac{6C3}{85C3}=0.00020$

(b) The probability that none are defective is:
$P(0)=\frac{79C3}{85C3}=0.800$
Therefore the probability that at least one is defective is:
1 - 0.800 = 0.200