A researcher receives 100 containers of oxygen. Of those containers , twenty of

Question

A researcher receives 100 containers of oxygen. Of those containers , twenty of them have oxygen that is not ionized and the rest are ionized.Two samples are randomly selected , without replacement, from the lot.
a)what is the probability that the first one selected is not ionized?
b) what is the probability that the second one selected is not ionized given that the first one was ionized?
c)what is the probability that both are ionized?
d)How does the answer in part (b) change if samples selected were replaced prior to the next selection?

Explanation / Answer

(a) P(the first one selected is not ionized) =20/100 =0.2 (b) P(the second is not ionized given the first one was ionized) = 20/99 = 0.202 (c) P(both are ionized) = P(the first one selected is ionized) X P(the second is ionized given the first one was ionized) = (80/100) X (79/99) = 0.638 (d) If samples selected were replaced prior to the next selection, P(the second is not ionized given the first one was ionized) = 20/100 = 0.2. The event of the first selection and the event of the second selection are independent.

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