The Thnoods of Thnoodville love their marbles, and other round things. In fact, each adult Thood belongs to exactly one of two clubs: 68% belong to the Billiards club and 32% belong to the Bowling club. Moreover, each day. . . . 43% of the members of the Billiards club has a red marble in their pocket, and . 77% of the members of the Bowling club has a red marble in their pocket. (a) If a random (adult) Thnood is observed, what is the probability that they belong to the Billiards club and have a red marble in their pocket? (b) If a random (adult) Thnood is observed, what is the probability that they have a red marble in their pocket? If a random (adult) Thnood is observed with a red marble in their pocket, what is the probability that they belong to the Bowling club?

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