Gabbar Probability

Gabbar Gunshots Probability Analysis

Everyone must have watched movie Sholay(1975). Do you remember the entry scene of Gabbar Singh (Amzad Khan)?

"Kitne Aadmi The"

Exactly That was the scene. In this scene Gabbar kills three of his henchmen. Lets skip the middle conversation and jump to this part.
Gabbar drags a revolver from one of his man and asks the number of bullets in it.
He replies "six". Generally a revolver has 6 bullets compact in a round structure.
 

Here the game begins.

He already made up his mind to kill all three men because he doesn't like coward people but he does not want to shoot them just like that. He wants some entertainment here.

This is the game of probability. He fires three bullets in the air to make remaining count three because he needs to kill only three people and one bullet is enough for each.

Now he revolves the cylinder of revolver in a speedy way so even he doesn't know where are the remaining three bullets.

Then he takes a shot towards each man. 3 chambers are with bullets and 3 are empty, he thinks there are 50-50 chances here.

Now lets analyze the situation here.

What we know
Three bullets are in a consecutive order and three empty chambers are also in consecutive order but it is a circle so any chamber can be its firing position. Only we can say confidently that there is no single empty chamber between two bullets. There is only one gap between two bullets and it is of three empty chambers.

Lets give names to each chamber. Suppose Chamber 1, Chamber 2 and Chamber 3 are empty chambers and Chamber 4, Chamber 5 and Chamber 6 are with bullets. We gave these names anti clock-wise because cylinder moves in clock wise direction so 2 will be fired after first and third will be fired after second and so on.

First shot can be empty or it can be with bullet. Nobody knows. Suppose if first shot is empty. It means either Chamber 1 or Chamber 2 or Chamber 3 in its firing position.

Suppose Chamber 1 is in its firing position during first shot then other two men will be saved because next number is of 2 and then 3 and both are empty chambers so all are saved (That's what happens in the movie)

Suppose Chamber 2 is in its firing position during first shot then second man will be saved because 3 is an empty chamber but 4 is filled with bullet it means last man (Kalia) will be killed. Even he ate salt of his master but no mercy would be here in first place.

 

Suppose Chamber 3 is in its firing position during first shot then second and third both men will be killed because 4 and 5 the chambers are with bullets.

 

Suppose Chamber 4 is in its firing position during first shot then all three will be killed because 4, 5 and 6 are with bullets.

 

Suppose Chamber 5 is in firing position during first shot then second will be killed and third man will be saved because 1 is empty.

 

Suppose Chamber 6 is in firing position during first shot then first and second both will be saved because 1 and 2 both are empty.

 

In this analysis, there are chances, each man can be killed and each can be saved. But can you predict what may happen with next?

You can't predict the future of first two men in any condition. You can predict the future of only last man and that's in two conditions only.
1) If First man is killed and second is saved
2) If first man is saved and second is killed

In first situation, you can easily find that chamber 6 was in firing position during first shot that's why first is killed and second is saved because second got chamber 1 which is empty. Now third man will get chamber 2 which is also empty and he will be saved too. There is no other condition for this situation.

In second situation, still you can find that chamber 3 was in firing position that's why first is saved and second is killed because second got chamber 4 which is with bullet. Now third man will get chamber 5 which is also with bullet and he will be killed too. There is no other condition for this situation too.

Both are unique situations.

Except these two conditions you can't predict future of third man.

Suppose first two are saved then you can't predict the fate of third.
He can be killed if chamber 2 was in firing position during first shot.
He can be saved if chamber 1 was in firing position during first shot.

Suppose first two are killed even then you can't predict the fate of third.
He can be killed too if chamber 4 was in firing position during first shot.
He can be saved if chamber 5 was in firing position during first shot.

Conclusion :
If second shot is different than first shot only then you can predict the behaviour of third shot.

Moral :
But after all none of this matters because eventually Gabbar would kill all three.

Fascinating Facts About Tigers

There is little doubt that tigers are some of the most beautiful, royal and scary animals nature has ever produced. They are incredible hunters, the biggest of all cat species (excluding the liger, which is a combination of lion and tiger) and can hunt in the water or land in equal measure.But if you think you know all there is to know about this magnificent animal, think again as you read this list of 22 fascinating tiger facts.

The Portrait of a Lady by Khushwant Singh

Khushwant Singh (2 February 1915 - 20 March 2014) was an Indian novelist and journalist. An Indo-Anglian novelist, Singh was best known for his trenchant secularism, his humor, and an abiding love of poetry. His comparisons of social and behavioral characteristics of Westerners and Indians are laced with acid wit. He served as the editor of several literary and news magazines, as well as two broadsheet newspapers, through the 1970s and 1980s. He was the recipient of Padma Vibhushan, the second-highest civilian award in India.

Story - The Portrait of a Lady

MY grandmother, like everybody’s grandmother, was an old woman. She had been old and wrinkled for the twenty years that I had known her. People said that she had once been young and pretty and had even had a husband, but that was hard to believe. My grandfather’s portrait hung above the mantelpiece in the drawing room. He wore a big turban and loose-fitting clothes. His long, white beard covered the best part of his chest and he looked at least a hundred years old. He did not look the sort of person who would have a wife or children. He looked as if he could only have lots and lots of grandchildren. As for my grandmother being young and pretty, the thought was almost revolting. She often told us of the games she used to play as a child. That seemed quite absurd and undignified on her part and we treated it like the fables of the Prophets she used to tell us.

She had always been short and fat and slightly bent. Her face was a criss-cross of wrinkles running from everywhere to everywhere. No, we were certain she had always been as we had known her. Old, so terribly old that she could not have grown older, and had stayed at the same age for twenty years. She could never have been pretty; but she was always beautiful. She hobbled about the house in spotless white with one hand resting on her waist to balance her stoop and the other telling the beads of her rosary. Her silver locks were scattered untidily over her pale, puckered face, and her lips constantly moved in inaudible prayer. Yes, she was beautiful. She was like the winter landscape in the mountains, an expanse of pure white serenity breathing peace and contentment.

My grandmother and I were good friends. My parents left me with her when they went to live in the city and we were constantly together. She used to wake me up in the morning and get me ready for school. She said her morning prayer in a monotonous sing-song while she bathed and dressed me in the hope that I would listen and get to know it by heart; I listened because I loved her voice but never bothered to learn it. Then she would fetch my wooden slate which she had already washed and plastered with yellow chalk, a tiny earthen ink-pot and a red pen, tie them all in a bundle and hand it to me. After a breakfast of a thick, stale chapatti with a little butter and sugar spread on it, we went to school. She carried several stale chapattis with her for the village dogs.

My grandmother always went to school with me because the school was attached to the temple. The priest taught us the alphabet and the morning prayer. While the children sat in rows on either side of the verandah singing the alphabet or the prayer in a chorus, my grandmother sat inside reading the scriptures. When we had both finished, we would walk back together. This time the village dogs would meet us at the temple door. They followed us to our home growling and fighting with each other for the chapattis we threw to them.

When my parents were comfortably settled in the city, they sent for us. That was a turning-point in our friendship. Although we shared the same room, my grandmother no longer came to school with me. I used to go to an English school in a motor bus. There were no dogs in the streets and she took to feeding sparrows in the courtyard of our city house.

As the years rolled by we saw less of each other. For some time she continued to wake me up and get me ready for school. When I came back she would ask me what the teacher had taught me. I would tell her English words and little things of western science and learning, the law of gravity, Archimedes’ Principle, the world being round, etc. This made her unhappy. She could not help me with my lessons. She did not believe in the things they taught at the English school and was distressed that there was no teaching about God and the scriptures. One day I announced that we were being given music lessons. She was very disturbed. To her music had lewd associations. It was the monopoly of harlots and beggars and not meant for gentlefolk. She said nothing but her silence meant disapproval. She rarely talked to me after that.

When I went up to University, I was given a room of my own. The common link of friendship was snapped. My grandmother accepted her seclusion with resignation. She rarely left her spinning-wheel to talk to anyone. From sunrise to sunset she sat by her wheel spinning and reciting prayers. Only in the afternoon she relaxed for a while to feed the sparrows. While she sat in the verandah breaking the bread into little bits, hundreds of little birds collected round her creating a veritable bedlam of chirrupings. Some came and perched on her legs, others on her shoulders. Some even sat on her head. She smiled but never shooed them away. It used to be the happiest half- hour of the day for her.

When I decided to go abroad for further studies, I was sure my grandmother would be upset. I would be away for five years, and at her age one could never tell. But my grandmother could. She was not even sentimental. She came to leave me at the railway station but did not talk or show any emotion. Her lips moved in prayer, her mind was lost in prayer. Her fingers were busy telling the beads of her rosary. Silently she kissed my forehead, and when I left I cherished the moist imprint as perhaps the last sign of physical contact between us.

But that was not so. After five years I came back home and was met by her at the station. She did not look a day older. She still had no time for words, and while she clasped me in her arms I could hear her reciting her prayers. Even on the first day of my arrival, her happiest moments were with her sparrows whom she fed longer and with frivolous rebukes.

In the evening a change came over her. She did not pray. She collected the women of the neighbourhood, got an old drum and started to sing. For several hours she thumped the sagging skins of the dilapidated drum and sang of the home coming of warriors. We had to persuade her to stop to avoid overstraining. That was the first time since I had known her that she did not pray.

The next morning she was taken ill. It was a mild fever and the doctor told us that it would go. But my grandmother thought differently. She told us that her end was near. She said that, since only a few hours before the close of the last chapter of her life she had omitted to pray, she was not going to waste any more time talking to us.

We protested. But she ignored our protests. She lay peacefully in bed praying and telling her beads. Even before we could suspect, her lips stopped moving and the rosary fell from her lifeless fingers. A peaceful pallor spread on her face and we knew that she was dead.

We lifted her off the bed and, as is customary, laid her on the ground and covered her with a red shroud. After a few hours of mourning we left her alone to make arrangements for her funeral. In the evening we went to her room with a crude stretcher to take her to be cremated. The sun was setting and had lit her room and verandah with a blaze of golden light. We stopped half-way in the courtyard. All over the verandah and in her room right up to where she lay dead and stiff wrapped in the red shroud, thousands of sparrows sat scattered on the floor. There was no chirruping. We felt sorry for the birds and my mother fetched some bread for them. She broke it into little crumbs, the way my grandmother used to, and threw it to them. The sparrows took no notice of the bread. When we carried my grandmother’s corpse off, they flew away quietly. Next morning the sweeper swept the bread crumbs into the dustbin.

                                         Khushwant Singh