Puzzle: Given 50 white marbles, 50 black marbles, and 2 boxes, put the marbles into the boxes to maximize the chances of selecting a black marble.
Sol: probability to select a box would be 1/2, so if we put 50 marbles in a box and other 50 in other box then probability to select black marble will be:
0.5*1 + 0.5*0 = 50%
Instead we can improve it by putting 1 black marble in a box and other 49 B+50 W marbles in other box.
Now probability for selecting a black marble will improve:
0.5*1 + 0.5*(49/99)= 74.5 %
and that is a significant improvement from previous 50%.
Please comment if it could be more improved.
Sol: probability to select a box would be 1/2, so if we put 50 marbles in a box and other 50 in other box then probability to select black marble will be:
0.5*1 + 0.5*0 = 50%
Instead we can improve it by putting 1 black marble in a box and other 49 B+50 W marbles in other box.
Now probability for selecting a black marble will improve:
0.5*1 + 0.5*(49/99)= 74.5 %
and that is a significant improvement from previous 50%.
Please comment if it could be more improved.
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