Question

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

Answer 1

(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.)

Answer 2

(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 3

This is binomial probability with p = 3/90. The customer chooses n = 3 cartridges, the probability 3 are defective is P(x = 3) = 3C3 * (3/90)^3 * (87/90)^0.

This is based on the binomial probability formula nCx * p^x * (1 - p)^(n - x).

For part B you want P(x >= 1) = P(x = 1) + P(x = 2) + P(x = 3), so find all 3 and add them together.

Answer 4

(a) This is sampling without replacement.
For the first selection the probability of selecting one that is defective is 5/90
For the second selection the probability of selecting one that is defective is 4/89
For the third selection the probability of selecting one that is defective is 3/88
\[P(3\ defective)=\frac{5\times 4\times 3}{90\times 89\times 88}=yoou can calculate\]

Answer 5

(b) The probability of selecting zero defective in a sample of 3 is
\[P(0\ defective)=\frac{85C3}{90C3}=\frac{87\times 86\times 85\times 84\times 83}{90\times 89\times 88\times 87\times 86}=0.84074\]
\[P(at\ least\ 1\ defective)=1.00000-0.84074=you\ can\ calculate\]