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Kebab Roulette

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 

Puzzle ID:#17391
Fun:*** (2.21)
Difficulty:*** (2.84)
Category:Probability
Submitted By:mad-adeAhu***
Corrected By:MarcM1098

 

 

 



Mad Ade was partaking in a game of "Kebab Roulette", where a large cannon with six chambers, like those of a revolver, can contain ammunition. In Kebab Roulette, five of the chambers are left empty and one is filled with salad, the most hated thing of all time served kebab eaters. The idea is to spin the chamber and then stand in front of the cannon while someone fires it at you. If there is no loser, there is a second round, where another load of salad is added, so now two chambers contain salad and the cannon is fired twice. If you are lucky and get an empty chamber, you can eat your kebab salad-free; if you are unlucky and get the salad-filled chamber, you must eat all the salad before eating your kebab.
The cylinder containing the six chambers is spun before the first shot. But it may or may not be spun after putting in the salad and after taking the first shot.
Which of the following scenarios has the lowest probability of being salad-free, and what is the value as a percentage?

Spinning the cylinder after putting in the salad and spinning it again after the first shot.

Spinning the cylinder only after putting in the salad.

Spinning the cylinder only after firing the first shot.

Not spinning the cylinder either after putting in the salad or after taking the first shot.

The probability of staying salad-free on the first shot is the same in all the cases.
Remember the cannon has six chambers.


Answer

The second scenario has the lowest probability of remaining salad-free, i.e. 40%. The fourth scenario has the highest probability of staying salad-free, i.e. 50%.

Scenario I:
The probability of remaining salad-free in the first shot = 4/6 = 2/3.
Since the cylinder is spun after the first shot, the probability of non-salad in the second shot = 4/6 = 2/3.
Hence, the probability of no salad in Scenario I = 2/3 * 2/3 = 4/9 = 44.44%.

Scenario II:
The probability of remaining salad-free in the first shot = 4/6 = 2/3.
Since the cylinder is spun after the first shot, the probability of non-salad in the second shot = 3/5.
Hence, the probability of no salad in Scenario II = 2/3 * 3/5 = 2/5 = 40.00%.

Scenario III:
The probability of remaining salad-free in the first shot = 4/6 = 2/3.
Since the cylinder is spun after the first shot, the probability of non-salad in the second shot = 4/6 = 2/3.
Hence, the probability of no salad in Scenario III = 2/3 * 2/3 = 4/9 = 44.44%.

Scenario IV:
The probability of remaining salad-free in the first shot = 4/6 = 2/3.
Since the cylinder is not spun after putting in the salad, both of the salads are in consecutive chambers. The probability of non-salad in the second shot = 3/4.
Hence, the probability of no salad in Scenario IV = 2/3 * 3/4 = 1/2 = 50.00%.

Thus, the second scenario has the lowest probability of remaining salad-free, i.e. 40%. The fourth scenario has the highest probability of staying salad-free, i.e. 50%.

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