Experimental Result:
The Excel web app below shows a simulation of the experiment, where the two bullets are placed randomly into two of the six chambers of the revolver.
For each experiment (after the 1st person pulled the trigger), both scenarios are considered and their outcomes recorded. The probability of each scenario can be calculated experimentally and it will reflect the theoretical probability when the experiment is conducted a lot of times (e.g. 1000). The more times the experiment is conducted, the closer it gets to the theoretical probability.
To activate the simulation, please key in a value from 1 to 10000 into the yellow cell in the Excel web app below and press "Enter".
Solution: Theoretical Explanation
Let the chambers be numbered from 1 to 6 and let the chamber spin such that 1 is followed by 2 followed by 3 and so on until 6 is followed by 1. We may assume that the bullets are placed in chambers 1 and 2.
If the first person gets a blank, then he would have triggered either chambers 3, 4, 5 or 6. If you do not spin the cylinder and pull the trigger, then you would have the following chambers as possibilities: 4, 5, 6 or 1 respectively. There are thus only 4 total possible outcomes, and only one (i.e. chamber 1) contains the bullet. Therefore, the probability of your phone surviving the shoot is \(\frac{3}{4} = 75\% \).
If you spin the cylinder, then pull the trigger, the probability of your phone surviving the shoot is \(\frac{2}{6} = \frac{1}{3} = 66.7\% \).
Hence, it is better not to spin the cylinder and pull the trigger as the probability of your phone surviving the shoot is higher.
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