You were captured and given one chance to escape with your life. You’re forced to play Russian Roulette with a 6-cylinder pistol. Each cylinder can hold 1 bullet. The gun has 2 bullets in it and the rounds were placed consecutively and the barrel was spun.
You took one shot and heard the click, luckily you didn’t get a bullet. You can choose to spin the barrel before the next shot. You want to live. Should you spin the barrel to improve your chances of survival?
You should not spin the barrel.
There are 2 consecutive bullets and 4 consecutive empty slots, so we let it be EEEEBB.
The probability that you get a bullet after spinning the barrel is 2/6 = 1/3.
You gained some knowledge after the first shot. Since you didn’t hit yourself you know you got one of the 4 empty bullet slots. The sequence is EEEEBB, so if you got the last E for the 1st shot, you will hit by a bullet in the 2nd shot. If you got any of the 1st three Es, you will not get a bullet in the 2nd shot. The chances of getting the 1st three Es is 3/4.
It’s safer to not spin the barrel again as the probability of missing the bullet is higher.