Suppose you have a jar with 14 red marbles and 26 black marbles. You randomly select a marble from the jar without replacement. If the marble is red, then you add 9 yellow marbles to the jar and randomly select another marble from the jar. If the first marble is black, then you add 13 blue marbles to the jar and randomly select another marble from the jar. Determine the probability of the following. (Enter each probability as a fraction.)
(a) the second marble is a black marble, given that the first marble was a red marble
(b) the second marble is a red marble, given that the first marble

Question

Suppose you have a jar with 14 red marbles and 26 black marbles. You randomly select a marble from the jar without replacement. If the marble is red, then you add 9 yellow marbles to the jar and randomly select another marble from the jar. If the first marble is black, then you add 13 blue marbles to the jar and randomly select another marble from the jar. Determine the probability of the following. (Enter each probability as a fraction.)
(a) the second marble is a black marble, given that the first marble was a red marble
(b) the second marble is a red marble, given that the first marble

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(c) the second marble is a yellow marble

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(d) the second marble is a blue marble