I'm abstracting the details of this question from actual life events.... but this is the basic gist of what I want to compute.

A friend of mine is playing a solo version of russian roulette, but with a twist.

The capacity of the revolver is 13 rounds.

Every position in the revolver holds a bullet.

The bullets are of poor quality and will only fire with a probability of 2%.

What is the probability that my friend will die if he attempts to pull the trigger 13 times.

Actually, I just saw the 'odds of 1 in a million' compounded thread.. which seems to be the same thing.. so is this right?

1 - (1 - 0.02) ^ 13 = 23%?

yep that's it

LOL,

no

A lot closer to 2%

Seriously people, 2% chance to fire everytime out of 13 how can you think its 23% ?

I think you misunderstood the question. The friend dies if any of the bullets are good, not every bullet. The chance of every bullet is 1 in 1 followed by 22 zeros, about the same a dealing four royal or king-high straight flushes in a row from well shuffled five card decks.

A simple guess would be that 2% chance of dying each time, times 13 chances, gives 26% chance of dying. It can't be 2%.

0.36 is the expected number of good bullets. That is, if you did this 100 times, firing at a target so on one gets killed, there would be close to 26 bullets that fire. But that doesn't meant that 26% of guns fire at least one bullet.

76.9% fire no bullets, 20.4% fire one, 2.5% fire two and 0.2% fire three. So the chance of dying is 20.4% + 2.5% + 0.2% = 23.1% = 1 - 76.9%. But the expected number of good bullets is 20.4%*1 + 2.5%*2 + 0.2%*3 = 26%.

Please tell your friend NOT to do this if you are serious...terrible idea. The ~23.1% chance is correct, assuming that whether one bullet fires is independent of another firing and assuming that the 2% number is accurate.

I doubt the real details actually involve a revolver because it's kinda hard to figure that the chance of it firing is EXACTLY 2%. Could easily be 5%, in which case, he may be in trouble.

Well If I read this correctly there is 1 chance out of 13 each time to fire a bullet and IF that happens then only 2% chance that the bullet actually fires.

So probability of this to happen is 1/13 * .02 = .0015.

Probability of a bullet never firing in 13 shots is .0015^13

Nope, OP said that all chambers are full, and his friend is firing 13 times. Not just one chamber is full.

This is Polish roulette, not Russian.

wtf 13 round revolver? wouldnt this be a semi automatic handgun then... which would change a lot of assumptions.

Hey guys, was bored at work so I took the time to make a Monte Carlo experiment on MATLAB.

Check these results out...

Here is the code...

Here is the resulting graph with the Monte Carlo experiment Death Percentage:

I would've said less than the probability that we got all the way to post 12 before someone referenced Deer Hunter.

lmfao @ variance good, and variance bad. AWESOME chart. and the "polish roulette" comment was great as well.