A box contains 2 red marbles and 3 black marbles. Two marbles are drawn in succession without replacement. Find the following: a. Find the probability the second marble is red? b. Find the probability that both marbles are the same color? c. Find the probability that the second marble is black given the first marble is red? d. Find the probability that first marble red given that the second marble is red?

b. The probability that both marbles are the same color is 4/15, since there are two ways that this could happen (both red or both black) and there are 15 possible outcomes in total.

c. The probability that the second marble is black given the first marble is red is 3/4, because out of the 4 possible outcomes (RR, RB, BR, BB) the only way to get a black marble on the second draw is if it is BR.

d. The probability that the first marble is red given that the second marble is red is 2/3, because out of the 3 possible outcomes (RR, RB, BR) the only way to get a red marble on the first draw is if it is RR or RB.

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