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Marbles

Permanent link to this puzzle: mscroggs.co.uk/puzzles/95
A bag contains \(m\) blue and \(n\) yellow marbles. One marble is selected at random from the bag and its colour is noted. It is then returned to the bag along with \(k\) other marbles of the same colour. A second marble is now selected at random from the bag. What is the probability that the second marble is blue?

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If you enjoyed this puzzle, check out Sunday Afternoon Maths LIX,
puzzles about spheres, or a random puzzle.
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