Two bullets

Question:

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?

image

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C

A

P

T

A

I

N

I

N

T

E

R

V

I

E

W

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Solution:

Since there are 6 total slots with 2 bullets, the probability of firing a bullet after shuffle is 2/6.

The probability of getting bullet without shuffle is 1/4. To understand this, look at the image, and imagine that one of the empty slots (3,4,5,6) just got shot. Now assuming the barrel turns clockwise, next shot will be 4, 5, 6 or 1. and out of these four, only (1) has the bullet. Hence the probability of firing a bullet is 1/4. Note that this same case stands in the anticlockwise direction.

With shuffle its 2/6=1/3. Hence yes, shuffling does increase probability of shooting bullet (from 1/4 to 1/3)

image

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