imagine a population of balls in which all are red except for three green ones. If we randomly sample two balls, with replacement, and the probability of getting green both times is p=0.04, which of the following is the number of red balls in the population?
14.imagine a population of balls in which all are red except for three green ones. If we randomly sample two balls, with replacement, and the
Let R be the number of red balls in the population. Then, the probability of getting a green ball on any one draw is (3 / (R + 3)), since there are 3 green balls in the population and R red balls. Since the sampling is done with replacement, the probability of getting green both times is:
P(Green both times) = P(Green on first draw) x P(Green on second draw)
P(Green both times) = (3 / (R + 3)) x (3 / (R + 3))
P(Green both times) = 9 / ((R + 3)^(2))
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