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P(R|X) = 4/7 P(B|X) = 3/7
P(R|Y) = 5/9 P(B|Y) = 4/9
P(R|Z) = 1/2 P(B|Z) = 1/2
P(R|X)*P(R|Y)+P(B|Z) + P(B|X)*P(R|Y)+P(R|Z) + P(R|X)P(B|Y)+P(R|Z) = (4/7)(5/9)(1/2) + (3/7)(5/9)(1/2) + (4/7)(4/9)*(1/2) = 10/63 + 15/126 + 8/63 = 36/126 + 15/126 = 51/126 = 17/42
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Day 2: Basic Probability Puzzles #3
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P(R|X) = 4/7 P(B|X) = 3/7
P(R|Y) = 5/9 P(B|Y) = 4/9
P(R|Z) = 1/2 P(B|Z) = 1/2
P(R|X)*P(R|Y)+P(B|Z) + P(B|X)*P(R|Y)+P(R|Z) + P(R|X)P(B|Y)+P(R|Z) = (4/7)(5/9)(1/2) + (3/7)(5/9)(1/2) + (4/7)(4/9)*(1/2) = 10/63 + 15/126 + 8/63 = 36/126 + 15/126 = 51/126 = 17/42