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Difficulty: MediumPuzzle Details

You are given 50 white marbles and 50 black marbles along with two jars.

You are asked to place all 100 marbles into the jars in any way you choose.

Afterwards, you will be blindfolded, the jars will be shaken and rearranged, and you will be asked to select just one marble (from either jar).

How would you arrange the marbles originally to maximise the probability of drawing a white marble?

Show Hint Show Answer Print Puzzle
[Ref: ZNSX]  

Answer:
Place one white marble in the first jar and place the remaining 49 white and 50 black marbles in the second jar.

This placement gives a large increase in the chances of drawing a white marble.

The probability of selecting either jar is 0.5, the probability of drawing a white marble from one jar is 1 and from the other jar is 49/99.

Therefore the overall probability is 0.5 x (1) + 0.5 x (49/99) = 0.74747.


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