A shelf in the Metro Department Store contains 90 colored ink cartridges for a popular ink-jet printer. Five 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.)

Question

Mathematics

Fiona Griffith

17 September, 22:40

A shelf in the Metro Department Store contains 90 colored ink cartridges for a popular ink-jet printer. Five 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.)

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Answers (1)

Know the Answer?

Gracie Bishop · Answer 1

A)

P (x = 3) = 5/90 * 4/89 * 3/88 = 1 / 11,748 = 0.000085

b)

Probability of selecting zero defective cartridges:

P (x = 0) = 85/90 * 84/89 * 83/88 = 592,620 / 704,880 = 0.840739

P (at least 1 defective) = 1 - 0.840739 = 0.159261