Many years ago in the far off land of Chanzania, a prisoner was to be executed. The king of Chanzania was a sporting fellow who thought highly of good thinkers. The king offered the prisoner a chance for freedom. He was given 100 black balls and 100 white balls, and was told to distribute them any way he liked. He was then blindfolded and told to draw a ball at random from one of the urns. If he drew a black ball he would be executed. If he drew a white ball, he would have his freedom. ( The urns were rearranged.) The prisoner was smart so he was set free. How would you have distributed the ba;;s in the three urns?
I know how to do it. I just need the answer with the highest pro bability!
2007-11-20 08:45:48 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Hi there
I think I would have put one white ball in urn #1, one white ball in urn #2 and all the rest in urn #3. This way my probability of drawing a white ball would be:
1/3 * 100% (if I draw from urn #1)
1/3 * 100% (if I draw from urn #2)
1/3 * 98/198 (if I draw from urn #3)
Overall, this yields a probability of a white draw of
just over 83%
Any other strategy is likely to be riskier!
2007-11-20 08:54:58 · answer #1 · answered by Anonymous · 2⤊ 0⤋
He put 1 white ball in one urn (100% probability of going free)
In the other there are 99 white and 100 black (99/199 = 49.75% probability of going free).
He now has a 50/50% chance of picking the urn. Half the time he will be the 100% urn and go free. The other half of the time he will pick the 49.75% urn.
0.5 x 1.0 + 0.5 x 0.4975 = 0.74875
That works out to a probability of nearly 75% which is much better than any other distribution.
2007-11-20 08:51:11 · answer #2 · answered by Puzzling 7 · 0⤊ 0⤋
I would put 1 black ball in 1 urn, 1 black ball in a second urn, and the remaining 98 black balls and 100 white balls in the 3rd urn.
Then my chances of picking a black ball would be 2/3 plus 98/200 X 1/3 = 0.49 X 1/3
overall, 0.83
2007-11-20 08:57:29 · answer #3 · answered by Joe L 5 · 0⤊ 0⤋
Assuming the prisoner knew what the challenge would be, the easiest way would be to put all 100 balls of one color into one urn, and 50 each of the other color balls in each of the other two. That way he would know by the level of the balls in the container which color they were. Odds of successfully choosing the correct ball: 100%!
2007-11-20 09:02:37 · answer #4 · answered by Anonymous · 1⤊ 0⤋
Put one white ball into one urn and the rest into the other. Upon placing your hand into an urn, if there is more than one ball, don't draw - pick from the other urn. Probability of survival is 1.
2007-11-20 08:52:58 · answer #5 · answered by richarduie 6 · 2⤊ 1⤋