1. The option of spinning the chamber to make it random again gives you a probability of surviving of 67% (1 - Probability of having a bullet in the chamber). The option of taking the gun as it is for a second attempt gives you a probability of surviving of 60% (1- Probability of having a bullet in the chamber after a first non-bullet attempt). Therefore, spinning the chamber to make it random again gives you a better chance of surviving.
2. The option of spinning the chamber to make it random again gives you a probability of surviving of 83% (1 - Probability of having a bullet in the chamber). The option of taking the gun as it is for a second attempt gives you a probability of surviving of 80% (1- Probability of having a bullet in the chamber after a first non-bullet attempt). Therefore, spinning the chamber to make it random again also gives you a better chance of surviving with only one bullet.
Step-by-step explanation:
1. Which option gives you a better chance of surviving?
Let's assume the gun has six chambers, so the probabilities are:
Number of bullets remaining/Number of chambers
For the first attempt, probabilities are = 2/6 or 33%
For the second attempt of shooting the gun, the probability of having a bullet in the chamber would be = 2/5 or 40%
On the other hand, if you spin the chamber to make it random again, the probability of having a bullet in the chamber would be = 2/6 or 33%
The option of spinning the chamber to make it random again gives you a probability of surviving of 67% (1 - Probability of having a bullet in the chamber). The option of taking the gun as it is for a second attempt gives you a probability of surviving of 60% (1- Probability of having a bullet in the chamber after a first non-bullet attempt). Therefore, spinning the chamber to make it random again gives you a better chance of surviving.
2. What would the answer be if there was only 1 bullet instead?
Number of bullets remaining/Number of chambers
For the first attempt, probabilities are = 1/6 or 17%
For the second attempt of shooting the gun, the probability of having a bullet in the chamber would be = 1/5 or 20%
On the other hand, if you spin the chamber to make it random again, the probability of having a bullet in the chamber would be = 1/6 or 17%
The option of spinning the chamber to make it random again gives you a probability of surviving of 83% (1 - Probability of having a bullet in the chamber). The option of taking the gun as it is for a second attempt gives you a probability of surviving of 80% (1- Probability of having a bullet in the chamber after a first non-bullet attempt). Therefore, spinning the chamber to make it random again also gives you a better chance of surviving with only one bullet.
