2 Suppose a random sample of size 2 is to be selected from a

2. Suppose a random sample of size 2 is to be selected from a lot of size 150, and it is known that 115 of the 150 items are good. The sample is taken in such a manner that the rst item is observed and replaced before the second item is selected (that is, the sample is taken with replacement\").

(a) What is the probability that both of the observed items are good?

(b) How would your answer in part (a) change if the sample is taken without replacement\"?

Solution

a)

P(both good) = P(good) P(good) = (115/150)(115/150) = 0.587777778 [answer]

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b)

The probability that the second is good will now be 114/149, as 114 are good out of 149.

Thus,

P(both good) = P(first is good) P(second is good) = (115/150)(114/149) = 0.586577181 [answer]