SOLUTION: The first urn contains 4 red marbles and 6 green marbles. The second urn contains 7 red marbles and 2 green marbles. Two marbles will be drawn from the first urn at random and imme

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Question 1203576: The first urn contains 4 red marbles and 6 green marbles. The second urn contains 7 red marbles and 2 green marbles. Two marbles will be drawn from the first urn at random and immediately put into the second urn without observing the color. Then, one marble will be drawn at random from the second urn. Find the probability that the second drawing turns out to be a red marble given that the first draw turns out to have the same color.
Answer by greenestamps(13206) About Me  (Show Source):
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P(2 reds drawn from first urn) = C%284%2C2%29%2FC%2810%2C2%29=6%2F45=2%2F15

P(2 greens drawn from first urn) = C%286%2C2%29%2FC%2810%2C2%29=15%2F45=1%2F3

P(2 marbles of same color drawn from first urn = 2%2F15%2B1%2F3=2%2F15%2B5%2F15=7%2F15

P(2 reds drawn from first urn and red drawn from second urn) = %282%2F15%29%289%2F11%29=18%2F165=6%2F55

P(2 greens drawn from first urn and red drawn from second urn) = %281%2F3%29%287%2F11%29=7%2F33

P(2 drawn from first urn are same color and red drawn from second urn) = 6%2F55%2B7%2F33=18%2F165%2B35%2F165=53%2F165

P(red drawn from second urn, given that 2 drawn from first urn are same color) = %2853%2F165%29%2F%287%2F15%29=%2853%2F165%29%2F%2877%2F165%29=53%2F77

ANSWER: 53/77