A shelf in the Metro Department Store contains 70 colored ink cartridges for a popular ink-jet printer. Seven of the cartridges are defective. If a customer selects 2 of these cartridges at random from the shelf, what are the probabilities that both are defective and at least 1 is defective?
A) 0.029, 0.100
B) 0.009, 0.100
C) 0.100, 0.809
D) 0.100, 0.191
E) 0.009, 0.191

Question

A shelf in the Metro Department Store contains 70 colored ink cartridges for a popular ink-jet printer. Seven of the cartridges are defective. If a customer selects 2 of these cartridges at random from the shelf, what are the probabilities that both are defective and at least 1 is defective? ​
A) 0.029, 0.100
B) 0.009, 0.100
C) 0.100, 0.809
D) 0.100, 0.191
E) 0.009, 0.191

Quizplus · Accepted Answer

The probability that both cartridges are defective is calculated by taking the probability of selecting one defective cartridge and multiplying it by the probability of selecting another defective cartridge, given that the first one was already selected. This is $\frac{7}{70} \times \frac{6}{69} = \frac{1}{10} \times \frac{2}{23} = \frac{2}{230} = 0.0087$, which rounds to 0.009.The probability that at least one is defective is calculated by finding the probability that neither of the two cartridges selected is defective and subtracting that from 1. The probability of selecting a non-defective cartridge twice is $\frac{63}{70} \times \frac{62}{69} = \frac{9}{10} \times \frac{62}{69}$, which simplifies to approximately 0.809. Subtracting this from 1 gives 0.191.

A Shelf in the Metro Department Store Contains 70 Colored