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Box A contains 6 red balls and 3 green balls, whereas box B contains 3 red ball and 15 green balls.
Stage one. One box is selected at random in such a way that box A is selected with probability 1/5 and box B is selected with probability 4/5.
Stage two. Finally, suppose that two balls are selected at random with replacement from the box selected at stage one.
g) What is the probability that both balls are red?
h) Given that both balls are red, what is the probability they came from box A?
i) What is the probability that one ball is red and the other is green?
j) Given that one ball is red and the other is green, what is the probability they came from box A?
In: Statistics and Probability