## 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 One of the jars will be chosen at random; then 1 marble will be withdrawn from that jar at random.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).

i didnt understand the solution dr…

Sure.. But tell me which part of the solution u didnt undrstnd?

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

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….

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.