Question
In a white box there are 7 red, 5 blue, and 8 black
marbles while in a black box there are 6 red, 9 blue, and 5 black marbles. One marble is drawn at random from the combined marbles of both boxes. Find the probability that it is a blue marble from the black box.Solution
Total marbles in white box = 7 + 5 + 8 = 20
Total marbles in black box = 6 + 9 + 5 = 20
Total marbles combined = 20 + 20 = 40
Probability marble is from black box = 20/40 = 1/2
Probability marble is blue given black box = 9/20
Required probability = (1/2) × (9/20) = 9/40
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