Marbles

You have two jars and 100 marbles. Fifty of the marbles are red, and 50 are blue. One of the jars will be chosen at random; then 1 marble will be withdrawn from that jar at random. How do you maximize the chance that a red marble will be chosen? (You must place all 100 marbles in the jars.) What is the chance of selecting a red marble
when using your scheme?

Solution

You really don’t need all 50 red marbles in jar A. One marble would do just as well. In
that case, there is still a 50 percent chance that jar A, containing a lone red marble, will be chosen. Then the 1red marble will be “chosen” at random — not that there is any choice. That yields a 50 percent chance of choosing a red marble just for jar A. You still have 49 more red marbles, which you can and must put in jar B. In the event jar B is chosen, you have nearly an even chance of drawing a red marble. (Actually the chance is forty-nine in ninety-nine.)

The total chance of selecting a red marble with this scheme is just under 75 percent (50 percent + 1/2 of 49/99, which comes to about 74.74 percent).

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Comments
  1. sushmita says:

    i didnt understand the solution dr…

  2. Divya.k says:

    oh god ! it really needs deep thinking. please upload some more similar puzzles

  3. revathy says:

    please explain me…so deeply…cant get it….through ths puzzle….how there will be 50% chance to draw the red marble in jar A..after a random choose….

  4. Revathy,

    In our configuration, we have one red marble only in Jar A. And all other marbles are in Jar B.

    The probability of the event of reaching a marble in Jar A is 0.5(as there are only 2 jars. so p=1/2)
    And if the user picks marble from jar A, then it must be red. As there is only one red.
    So that is how its 50%. Hope you understood now.

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