A bag contains 4 red balls and 8 green balls. (a). (5’) Three balls are selected...

A bag contains 4 red balls and 8 green balls.

(a). (5’) Three balls are selected from the bag randomly. What is the probability that 1 red ball and 2 green balls are selected?

(b). (10’) Three balls are selected from the bag sequentially without replacement, and the first ball is discarded without observing the color. If the third ball is green, what is the probability that the second ball is red?

(c). (10’) Two balls are selected from the bag randomly. Suppose that you win 3$ for each red ball selected and 1$ for each green ball selected, compute the probability distribution (i.e., probability mass function) and the expected value of the winnings.

(d). (10’) You pick up a ball randomly, and put it back in the bag. You repeat the above procedure for n times. If X of n balls picked are red, you win 3X dollars. Assume that you need to buy a ticket before starting to pick up balls, what is the expected value of a ticket? (Hint: the expected value represents the break-even costs, i.e., the amount of money that you win, on average, per play.)

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Expert Solution

orchestra answered 1 year ago

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