Survive the Russian Roulette...!!!
Back to my favourite game of beating the odds, here is another one....Russian roulette...!!!
Unfortunately you have been captured by the enemy and taken as prisoner of war. Your life now depends on a crazy army colonel who loves to play the game of Russian roulette with his prisoners. If you can survive his game you might get a chance to breathe for few more days. Here is the game...
You have been tied to a chair and won't be able to get up. The colonel brings in a barrel of the gun, six chambers, all empty. He will let you watch him put two bullets into adjacent chambers in the gun. Closes the barrel and spins it for few seconds. He fires one shot in the air, CLICK...the chamber was empty. Now he points it to your head and asks if you prefer to spin the barrel again before pulling the trigger or just pull the trigger without spinning. Which one would you prefer to increase your chances of surviving this deadly game? Remember the gun still has 2 bullets.
posted by Rajesh Munavalli @ 2:12 PM
5 comments
5 Comments:
Your first part of analysis is correct. However your second part isn't quite right. Think about this statement of yours one more time.
After one escape the chances of being killed increases 2/5, while the chances of escaping again drops to 3/5. So to increase the chance of escaping again u better spin, if given a chance .. ofcourse.
[HINT: Consider conditional probability]
The following statement is not true. Any time you spin the barrel, the chances of getting an empty chamber is always 4/6 = 0.67. It does not depend on the previous spin.
On the other hand, if you spin it twice, you are relying on two independent probabilities. So chances of getting two Empty consecutively after each spin is 4/6 * 4/6 = 0.44
where 4/6 is the probability of getting an Empty barrel in one spin.
Think over again...!!!
As it stands now, you are looking at 2 out of five, since he has just removed on empty chamber from the game. Provided he gives it a hearty spin, at least you are back to two out of six.
Now I'm sure when you've got a revolver pointed at your head, lots of stress released chemicals make it hard to think, but I don't see any need for further analysis. 2 of 5 vs. 2 of 6 - I'd take 2 of 6.
I don't want to give out the answer. Here is something to put you in the right direction. If your question is what is the probability that I will survive two successive shots, then the answer is 0.44. This is the probability when you ask even before spinning the first time. But here you already know that the first shot was a miss i.e, probability of suriving in first spin is 1 (Remember, he didnt shoot you in first spin).
I would argue otherwise. I agree that every spin is independent of the previous spin. But for two successive spins to be empty is (probability of first spin to be empty) * (probability of second spin to be empty), which translates to 4/6 * 4/6 = 0.44.
This is synonymous to flipping a coin twice and the probablity of heads showing up on both occasions is 1/2 * 1/2 = 0.25.
That is the correct answer Praveen...
In other words, when you dont spin second time, the only time you will get shot is when the first shot was fired from the chamber which is adjacent to the chamber with the bullet. Out of 4 chambers only 1 can be adjacent. Hence the probability 3/4=0.75
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