Russian Roulette III - Gabbar Singh

Probability Level 2

In yesteryear blockbuster Hindi movie Sholay, Gabbar Singh is a fearsome dacoit leader who is upset with 3 of his underlings A, B and C. He fills up his 6 chambered revolver with 3 ADJACENT bullets. Then he spins the chambers and lines up his gun on dacoit A.

He pulls the trigger. The dacoit survives. What was the probability of survival of dacoit A?

Now Gabbar lines up the gun on Dacoit B without spinning the chamber. Click! The dacoit survives. Whats the probability of survival of dacoit B?

Finally Gabbar goes to dacoit C ( named Kaalia in movie). Pulls the trigger a third time without spinning. Dacoit survives. Whats the probability of survival of dacoit C?

Answer as probability of survival of dacoit A B C respectively.

3/4, 2/3, 1/2 1/2, 2/3, 1/2 1/2, 2/5, 1/4 1/2, 1/2, 1/2

2 solutions

Satyen Nabar
May 23, 2014

prob of survival of dacoit A = 3/6 = 1/2

The prob of survival of dacoit B depends upon what happens to dacoit A.

Let bullets be in chambers 4 5 6. since dacoit A survives, the chambers that were fired can be either 1 2 3.

So the next chamber to be fired is either 2 3 4 . Hence 2/3 chance of survival.

Since both dacoit A and dacoit B survive, the chambers fired can be either 1 2 or 2 3. Hence the next chamber fired is either 3 or 4. So Kaalia dacoit c is back to 1/2

Dear Pushpesh, since both dacoit A and B survive, the two chambers that could be fired ( considering bullets are in 4 5 6 ) would be 1 and 2 or 2 and 3.

Satyen Nabar - 7 years ago

thanks : )

PUSHPESH KUMAR - 7 years ago

why have you written- "Since dacoit B survives, the chambers fired can be either 1,2 or 2,3." It should be 1,2 or 1,3 because either of 2 or 3 was fired on B for his survival "Hence, the next chamber fired is either 2/3(one that was not fired on dacoit B) or 4." If i am wrong then please remove my doubt. It will be great for me. But your answer is definitely correct.

PUSHPESH KUMAR - 7 years ago

how can it be in 1 and 3. They must be consecutive.

Mihir Dahiya - 6 years, 7 months ago

Maharnab Mitra
May 26, 2014

For shooting A, there are 3 chances of getting shot and 3 chances of getting missed. So, the probability of missing the shot is $\frac{1}{2}$ . I have shown only the favourable cases.

For shooting B, we have to consider that A has survived. So, according to the figure below, probability of missing B is $\frac{2}{3}$ .

For shooting C, we have to consider A and B both have survived. So, according to the figure below, probability of missing C is $\frac{1}{2}$ .

And there goes the famous dialogue before killing Kaalia : "Ab tera kya hoga, Kaalia?" (Now what will happen to you, Kaalia?). And after missing the 3rd shot, he laughs, turns back to them and shoots all of them down! An great movie!

Maharnab Mitra - 7 years ago

Russian Roulette III - Gabbar Singh

2 solutions

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