A shelf in the Metro Department Store contains 90 colored ink cartridges for a p

Question

A shelf in the Metro Department Store contains 90 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.)

Please go through steps to solve. I keep getting .01702 for the first answer but it is wrong.

Explanation / Answer

we are given

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

Six of the cartridges are defective

total cartridges =90

defective=6

(a)

probability of 1st one being defective =6/90

probability of 2 being defective =(6/90)*(5/89)

probability of 3 being defective =(6/90)*(5/89)*(4/88)

probability of 3 being defective is 0.00017..........Answer

(b)

we know that

probability of 1st one being defective =6/90

probability of 2 being defective =(6/90)*(5/89)

probability of 3 one being defective =(6/90)*(5/89)*(4/88)

probability that at least 1 is defective = probability of 1st one being defective+probability of 2 being defective+probability of 3 being defective

probability that at least 1 is defective =(6/90)+(6/90)*(5/89) + (6/90)*(5/89)*(4/88)

probability that at least 1 is defective =691/9790

probability that at least 1 is defective =0.071........Answer

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