Predictive Hacks

# Interview Question: A Variation of Russian Roulette

For Data Science positions, it is common to be asked questions about probabilities. One example is the following:

### The Question

Assume that we have a revolver (can take up to 6 bullets) where we have put 2 bullets in a row. Then we spin the cylinder, we pull the trigger and the weapon does not fire. We are about to try again. The muzzle is placed against you, would you spin the cylinder again in order to increase your chances to live?

This is a tricky question. If there was only one bullet in the cylinder, then the best strategy would be to spin it again, since at the first shot, the chances for the gun to fire is 1/6 and at the second time will be 1/5. But in our case, we are dealing with two bullets that are placed in a row. So, in the beginning, the chances for the weapon to fire were 2/6, i.e. 1/3. Thus, if the player decides to spin the cylinder again, the chances for the gun to fire will be again 1/3. However, we know that the gun didn’t fire the first time. But what does it mean in practice?

Assume that the bullets are placed at positions 1 and 2. Since the first trigger pull did not fire, it means that now the trigger is in one of the following positions: 4,5,6, and 1. So, the chances for the weapon to fire are 1/4. Since 1/4 is less than 1/3, the best strategy of the player is not to spin the cylinder.

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