probability

Question

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

 

a) If a customer selects 2 of these cartridges at random from a shelf, what is the probability that they are all defective?

 

(b) If a customer selects 2 of these cartridges at random from a shelf, what is the probability that at least 1 is defective?

Answer 1

a) The probability of picking a faulty cartridge is 5/85=1/17. The probability of picking a second faulty cartridge is 4/84=1/21. The combined probability is (1/17)(1/21)=1/357.

b) If P(x) is the probability of selecting x faulty cartridges, then P(2)=1/357.

P(1)=(5/85)(80/84)+(80/85)(5/84)=2(1/17)(20/21)=40/357. P(1≤x≤2)=P(1)+P(2)=41/357.