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Probability of Firing Bullet
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probability of firing bullet puzzle

Two bullets are put into a gun's round barrel consecutively, which has capacity of 6. The gun is shot once, but no bullet is fired.
Does rolling the barrel (shuffling) before next shot increase the probability of firing a bullet?

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Case 1: Probability of firing after shuffling(Rolling the barrel)
Out of 6 total slots, We have bullets in 2 consecutive slots. So the probability of firing after shuffling the barrel is 2/6 = 1/3

Case 2: Prabability of firing without shuffling
In this case the first shot is already made on one of the emply slots. So imagine we have bullets in Slots 1 and 2
and the other 4 slots (3,4,5,6) are empty.Now assumming the barrel turns clockwise, next shot will be 4 ,5 ,6 or 1.
and out of these four, only (1) has bullet.

Hence the probability of firing a bullet without shuffling the barrel is 1 out of 4, ie 1/4
Suppose the barrel turns anticlockwise, then also the probability of firing remains same.

So shuffling the barrel before next shot increases the probability of firing a bullet (as 1/3 > 1/4)

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