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P(R) = 3/7
P(B) = 4/7
P(R|B) = 3/6 = 1/2
P(R|Bc) = 2/6 = 1/3
P(Bc) = 1-4/7 = 3/7
P(B|R) = P(R|B) * P(B) / P(R|B) * P(B) + P(R|Bc) * P(Bc)
P(B|R) = { (1/2) * (4/7) } / { (1/2) * (4/7) + (1/3) * (3/7) }
P(B|R) = { (4/14) } / { (4/14) + (1/7) }
P(B|R) = { (4/14) } / { (4/14) + (2/14) }
P(B|R) = (4/14) / (6/14)
P(B|R) = (4/6)
P(B|R) = (2/3)
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Day 3: Drawing Marbles
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P(R) = 3/7
P(B) = 4/7
P(R|B) = 3/6 = 1/2
P(R|Bc) = 2/6 = 1/3
P(Bc) = 1-4/7 = 3/7
P(B|R) = P(R|B) * P(B) / P(R|B) * P(B) + P(R|Bc) * P(Bc)
P(B|R) = { (1/2) * (4/7) } / { (1/2) * (4/7) + (1/3) * (3/7) }
P(B|R) = { (4/14) } / { (4/14) + (1/7) }
P(B|R) = { (4/14) } / { (4/14) + (2/14) }
P(B|R) = (4/14) / (6/14)
P(B|R) = (4/6)
P(B|R) = (2/3)