You've stolen from King Arthur's flour reserves and been thrown in jail. The king is magnanimous, however, and rather than having you drawn and quartered on the spot, he allows you to play a little game.
You're given 100 marbles — 50 black and 50 white — and you must place them in two urns, in any way you like, as long as you obey the king's rules.
You must place all the marbles, and neither urn can be left empty. Each urn will be shaken so that the marbles are all jumbled up — the order in which you place them doesn't matter.
The king will then follow a simple procedure: he will pick an urn uniformly at random (i.e., either one is equally likely to be chosen); and from that urn, he will draw a marble uniformly at random. If it's white, you live; but if it's black, you'll be fed to the Haitians on a Neapolitan pizza, or perhaps drawn and quartered — the king hasn't yet made up his mind.
You could place all the white marbles in one urn, and all the black in the other, in which case your chances are fifty-fifty — but you can do better than that! If you place the marbles in the best way possible, what is your probability of survival?
You're given 100 marbles — 50 black and 50 white — and you must place them in two urns, in any way you like, as long as you obey the king's rules.
You must place all the marbles, and neither urn can be left empty. Each urn will be shaken so that the marbles are all jumbled up — the order in which you place them doesn't matter.
The king will then follow a simple procedure: he will pick an urn uniformly at random (i.e., either one is equally likely to be chosen); and from that urn, he will draw a marble uniformly at random. If it's white, you live; but if it's black, you'll be fed to the Haitians on a Neapolitan pizza, or perhaps drawn and quartered — the king hasn't yet made up his mind.
You could place all the white marbles in one urn, and all the black in the other, in which case your chances are fifty-fifty — but you can do better than that! If you place the marbles in the best way possible, what is your probability of survival?
THE Philosopher
You've stolen from King Arthur's flour reserves and been thrown in jail. The king is magnanimous, however, and rather than having you drawn and quartered on the spot, he allows you to play a little game. You're given 100 marbles — 50 black and 50 white —…
If you place the marbles in the best way possible, what is your probability of survival?
Anonymous Quiz
12%
51%
2%
62.5%
2%
66.5%
15%
66.67%
12%
74.5%
31%
74.75%
6%
87.5%
5%
87.75%
2%
99%
14%
100%