QUESTION 12 Mr. Spock investigates the flora on a new planet. Some of the plants have colorful blooms. For example, 35% of the flowers have red blooms and 20% of the flowers have blue blooms. After some experiments, Spock finds that 30% of all the plants on the planet are poisonous and 25% of the plants have medicinal properties. Let R = the flower has red blooms Let B = the flower has blue blooms Let X = the plant is poisonous Let M = the plant has medicinal properties Spock computes the following compound probabilities: 8 8 p(R and X) = 0.0875 p(B or M) = 0.325 Suppose you visit this planet and come upon a red flower. What is the probability that this plant is poisonous? X P(X | R ) = 0.30 0.35 = 0.857 O P(X | R ) = 0.35 + 0.30 0.35 = 1.857 O P( R |X ) = 0.35 0.30 = 1.167 O P( R | X ) = 0.0875 0.30 = 0.292 O P(X | R ) = 0.0875 0.35 = 0.250 O P(RIX ) = 0.35 + 0.30 0.30 = 2.167