RAY: In fact he can improve his chances by putting 99 marbles in one box, and one marble--a white one--in the other box. See, right away when the warden comes in, he's got a 50-50 chance of picking a box. So if he picks the one with the white marble in it, then the fellow is automatically going to improve his chances to 75 percent. If he picks the other box, then his chances are still pretty close to 50-50. So by rearranging the marbles in this peculiar way, he can improve his chances to almost 75 percent.
TOM: That's not bad. In fact his chances of losing, if I calculate correctly, are .05 times 50 over 99. That's 25 percent. A little more than 25 percent. That means that his chances of living are almost 75 percent.
[ Car Talk Puzzler ]