Suppose that a computer chip company has just shipped 5.000 computer chips to a

Question

Suppose that a computer chip company has just shipped 5.000 computer chips to a computer company. Unfortunately, 50 of the chips are defective. Compute the probability that two randomly selected chips are defective using conditional probability. The probability that the first randomly selected chip is defective is 50/5,000 = 0.01 = 1%. Compute the probability that two randomly selected chips are defective under the assumption of independent events. The probability is ____. (Round to eight decimal places as needed.) The probability is ____ (Round to eight decimal places as needed.) When small samples are taken from large populations without replacement, the assumption of independence does not significantly affect the probability. Based on the results, what does this mean? The probabilities are very different, but the probability found assuming independent events is larger, so it does not matter. The probabilities are very different, but the probability found assuming independent events is smaller, so it does not matter. The probabilities are exactly the same. The probabilities are nearly the same.

Explanation / Answer

a. so, that means we have to select 2 from 50
= 50C2 / 5000C2
= .00009802

b. This is getting 2 defective indepdently
= P(1stdefective)*P(2nddefective) [ assumed no replacement]
= .01*(1/99)
= .00010101

Answer is D. The probabilities are nearly the same.

The probabilities are so near that on finding probabilities withput replacments for very small samples ( here 50 out of 5000) the assumption of indepdentence doesn't make much of a difference.

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