2/3 for pulling the trigger again and 1/2 for spinning. You will have more chances in case of spinning.

Consider where the bullets could be so they are consecutive: (BBxxxx), (xBBxxx), (xxBBxx), (xxxBBx), (xxxxBB), (BxxxxB). You have a 2/3 chance of getting shot on pull number 1. If you respin you still have that same chance, assuming the spin is random. Now assume the first was a blank. Only 4 of the cases above will work, and in one of them you'll get shot on a second pull. So your chances of getting shot are 1/4 on the second pull without a respin Don't respin! The two consecutive bullets makes this an interesting case, but what it means is that after a first blank you know *neither* bullet was in that position. This tips the probabilities just enough to make the right answer counterintuitive. The answer is just the opposite if there is only 1 bullet. In that case you should respin.

There are only 4 ways to arrange the revolver with consecutive bullets so that the first shot is nothing. Out of those 4 there is only one way to arrange the revolver so the second shot kills. So for the 2 consecutive hammer pulls(granted the first trigger pull is empty) you have a 1/4 chance of getting shot. As for pulling the trigger and spinning the chamber and pulling again. That is a selection with replacement. The likelihood that the second shot will fire is the same as the likelihood that the first shot will fire. 2/6 or 1/3. Now the likelihood that you would pull the trigger on an empty chamber, spin chamber, pull the trigger on a loaded chamber is (4/6)*(2/6)=2/9

It matters how the bullets are loaded which is why the question stipulates that they are in adjacent chambers. If the bullets are not adjacent it is better to spin. Spinning gives a 2/6 chance of being shot and not spinning gives a 2/4 chance. With adjacent bullets, spinning produces the same odds as above, 2/6, but not spinning improves the odds to 1/4. Interview candidate is right.

I would take a different approach and check if the Gangster was right or left handed as I believe this plays a part... The combined weight of two bullets will affect the position of where they come to rest. If he's right handed he will tilt the weapon to the right in order to spin the cylinder with his left hand, the likelihood is that the bullets will come to rest at the bottom right so that when he pulls the trigger the bullets are 'further' from the firing position. However if he's a south-paw, the odds are drastically reduced as he will tilt the weapon to the left whilst loading resulting in a greater likelihood that the 2nd bullet will kill you. So I'm gonna ignore the odds and go with my gut! Take the chance of a second trigger pull for the righty and take a second spin for the lefty. Any way it's a dumb question, the chances are he's using a Makarov, which is semi-automatic, so you'll never survive the first shot. Statistically though (and just for the record) you should always take the second shot as the interviewee got the answer right... BTW I'm not a gun nut, I just watch a lot of crap movies!

'1/4 for pulling the trigger. 1/3 for spinning and pulling the trigger.' =candidate is right Probabilities for 'next shot'=kill 1/4 (no spin) or 3/12 2/6 (spin) or 4/12 or 1/3 so, for (no spin) the probability of getting shot is lower (1/4, because first pull = empty, means he hit 1 of 4 empty ones. As he puts the bullets in consecutive orders, 3/4 empty will be followed by another empty one. 1/4 will be followed by a bullet) (2/6, if he spins, the probability stays the same, because he can hit again the same empty one)

1/4 for pulling the trigger again and 1/2 for spinning. You will have more chances in case of spinning.