I've been a Mathematics enthusiast during all my days as a student, and I was used to looking for challenging problems to solve. I'm busy with my career now, so I rarely get a chance to refresh my skills in math.
The moment I came across this mind game contest by @jaycee7viral, I immediately took out my pen and paper to see if I still have those unused abilities that I've been hiding for so long. :)
Although I'm not that good in probability, I'm a big fan of it and I've come across a lot of tricky problems within the scope of this math field, but it happened way long ago. So when I saw this mind-boggling problem, it took me several minutes of intensive analysis, until I found a clue which led me easily to a confident answer: There isn't a condition that the contents of two bowls should be equal in marble counts.
Solution:
Applying the concepts of probability on mutually inclusive and exclusive events, and tapping them to the problem, we get a general formula for the probability of living, that is:
If we take a look at the equation, there are two parameters that should be at their maximum values to obtain the maximum possible chance for the prisoner to survive:
The maximum value of any probability is one (1) and it will never go higher than that.
Thus, one of the bowls should have a probability of one, and to do that, the contents must be all red.
Below is a tabulation of all the possible situations wherein one of the bowls contains all red marbles and the corresponding probability for each condition.
Therefore, in order for the prisoner to have the highest chance for saving his life, he has to divide it this way: Put only one red marble to one bowl, and the other 99 (49 red and 50 black) to the other bowl.
Have you submitted your entry to this #mindgamescontest? Follow @jaycee7viral and read his ongoing challenge here. If you can come up with a probability higher than 74.75%, you take the prize! Haha! Good luck! :)