A shipment of 50 personal computers has 40 intact, eight damaged but operative,

Question

A shipment of 50 personal computers has 40 intact, eight damaged but operative, and two inoperative. If two personal computers are randomly selected without replacement from the shipment, (a) what is the probability that both are intact? (b) What is the probability that both are damaged but operative? (c) If you were returning the first personal computer to the shipment before selecting the second, what would be your answers in (a) and in (b)? (d) If three personal computers were to be selected without replacement, what is the probability that all three are damaged but operative? (e) What would be your answer to (d) if you sampled with replacement?

Explanation / Answer

Solution:

Given In the question

Total no. of Computers = 50

Intact computers = 40

Operative and Damaged = 8

Inoperative = 2

a) Probability of intact computers = (40/50) * (39/49) = 0.8 * 0.7959 = 0.6372 or 63.72 %

b) Probability of Both Damaged and Operative = (8/50) * (7/49) = 0.16 * 0.1428 = 0.022848 or 2.228%

(c) After returning the Computer part (a) answer would be = (40/50) * (40/50) = 0.8 * 0.8 = 0.64 or 64%

part (b) answer would be = (8/50) * (8/50) = 0.16 * 0.16 = 0.0256 = 2.56%

(d) Probability of three damaged and Operative =( 8/50)*(7/49)*(6/48) = 0.16 * 0.1428 * 0.125 = 0.002856 or 0.2856%

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