Think you know probability?

[megamuel]

Haha...Aim.... Good one! Nah my night was crap, been working, had a few drinks, not tired yet.... Also a bit of insomnia but sleeping pills + alcohol = no good. Hows your job going at the prop firm? You started yet?

Sam.

 

[Skill Leverage]

Start in 2 weeks mate; in the meantime I will be moving daan Saaf, playing Gears of War and teaching people how to avoid blowing their brains out among (few) other things.

 

[megamuel]

Cool, do you have to be a good trader to get a job at a prop firm or do they train you to become one? Where abouts are you from now?

 

[Skill Leverage]

PM'ing you so as not to derail the thread

 

[frugi]

Hello Skill L,

You have two bullets next to each other in a 6-barrel gun. This means there is a series of 4 chambers containing no bullets. You pull the trigger once. Nothing happens. This means that you pulled the trigger on one of the 4 empty chambers. Since the cylinder rotates only one chamber, the ONLY one of these 4 where a bullet could have rotated to the firing position is the one directly adjacent to the two bullets. If the first pull of the trigger was on any of the 3 other empty chambers, another empty chamber must rotate to the firing position - you survive.

If you re-spin the chambers, your chance is only 66.66%, since you have once again randomised the firing chamber - the chances of surviving are 4 in 6 (4 empty chambers, 2 bullets).

Spot on.

There is therefore a 3 in 4 chance that you will survive if you pull the trigger again - 75%.

I think this is wrong. Yes there are 3 safe empties out of 4, but you have already selected one of them on your first pull, so you must refer to the probability applicable to that pull, namely 1/6 (as the game starts with a random spin).

To put it another way, the second pull doesn't randomly select one of the four empty chambers, it selects the next chamber, so what is important is the odds of selecting the only chamber before the first bullet on the first spin.

As this is 1/6, I think you're twice as likely to live if you pull again.

But (and this is what I find interesting about the problem):

You are handed a revolver, with two bullets placed in adjacent chambers in the 6-chamber cylinder. The cylinder is spun to a random position and the loaded gun is handed to you. You put the barrel to your head and pull the trigger - an empty click.

My answer supposes that the first spin and pull could have resulted in death (although on this occasion it hasn't). As the question clearly states "the cylinder is spun to a random position", it is a fair expectation.

But if the problem-setter insists this can't happen (i.e. the first spin is actually not random, because it always lands on an empty chamber) then I defer to your and others' answer of 1/4, albeit with a complaint that the question is now self-contradictory.

 

[Skill Leverage]

I think this is wrong. Yes there are 3 safe empties out of 4, but you have already selected one of them on your first pull, so you must refer to the probability applicable to that pull, namely 1/6 (as the game starts with a random spin).

There are 4 possible configurations of the cylinder in which two adjacent bullets can be placed, and the trigger pulled once to produce a click. Out of these, only one will kill you on a second pull of the trigger. You have not 'selecteded' any of these configurations with your first pull of the trigger, because before the first pull of the trigger none of these configurations existed.

Your chances of survival are 75%.

 

[frugi]

Yes I see now. The fact that you don't die on the first pull yields further information and removes two of the six possible initial configurations. Cheers for a good problem!

 

[Skill Leverage]

Yay, someone who listens There's hope for us all

 

[megamuel]

sorry i got it wrong coz i dont know what adjacent means haha. now if the bullets where in opposite chambers it would then be 50/50

I too thought adjacent meant opposite But what are you saying would be 50/50?

Someone correct me if I am wrong but whether the 2 bullets are opposite or next to eachother, in both cases a re-spin would result in 4/6 (66.66...%) chance of survival. Whereas if you fire again, there is a 3/4 (75%) chance of survival if the bullets are next to eacother (adjacent) and a 2/4 (50%) chance of survival if the bullets were opposite?

So basically, if the bullets are opposite, spin again, if the bullets are next to eachother re-fire. Now someone please tell me I am stupid for not knowing the meaning of adjacent and not because I can't work out basic probability!

Sam.

P.S. Sorry Claudia...:innocent:

 

[Skill Leverage]

I too thought adjacent meant opposite But what are you saying would be 50/50?

Someone correct me if I am wrong but whether the 2 bullets are opposite or next to eachother, in both cases a re-spin would result in 4/6 (66.66...%) chance of survival. Whereas if you fire again, there is a 3/4 (75%) chance of survival if the bullets are next to eacother (adjacent) and a 2/4 (50%) chance of survival if the bullets were opposite?

So basically, if the bullets are opposite, spin again, if the bullets are next to eachother re-fire. Now someone please tell me I am stupid for not knowing the meaning of adjacent and not because I can't work out basic probability!

Sam.

P.S. Sorry Claudia...:innocent:

 

[frugi]

It is preferable to be challenged/refuted correctly and understand why than to bask in the certainty of ignorance. The latter may be more comfortable, but it's the former that leads to growth. As a trader I could not be more pleased by the poll results; as a human I find them mildly depressing.

 

[Skill Leverage]

Haha well said. What's most interesting to me from a behavioural standpoint is that 20 traders still chose re-spin, having been told the correct answer. This is truly amazing to me, and goes to show how stubborn traders can be in refusing to change their opinion, despite the information in front of them.

There you go Paul71, there's your relation to the markets you silly toss.

 

[Masquerade]

20 traders didn't choose re-spin.

 

[megamuel]

Haha well said. What's most interesting to me from a behavioural standpoint is that 20 traders still chose re-spin, having been told the correct answer. This is truly amazing to me, and goes to show how stubborn traders can be in refusing to change their opinion, despite the information in front of them.

There you go Paul71, there's your relation to the markets you silly toss.

I think most people would have voted before reading the asnwers....

 

[MrGecko]

What interests me is if the traders who don't understand probability (the 20) think in probabilities (vís a vís Mark Douglas).

 

[Skill Leverage]

Masq on the ball as ever with his 'I have nothing to contribute so I'll pick holes' banter...

You're right I misread the poll, 15 chose re-spin after being told. And I suppose some of them might not be 'traders' in the pure sense of the word. They do however, show a clear interest in being a successful trader, yet they can't analyse basic information that is in front of their faces.

That better for you Masq you sarcy d!ck?

 

[Skill Leverage]

But that's my point Megamuel, the information was there for them, and they chose not to use it. I suppose that would have ruined the exercise for them, but it's still an interesting point.

 

[Skill Leverage]

Might have come off as overly harsh on old Masq there. I'm over it though.

 

[Skill Leverage]

I suppose with this poll, most people answer before reading the other posts, so my point about them ignoring the truth might be invalid here. Still, more than 50% of people got the answer wrong, whether they knew it or not. Gecko makes a good point, and I imagine that most people don't know that they don't know probabilities. I've certainly seen that with poker, where people spout something they read in a book without any understanding of its implications.

 

[megamuel]

Yeah well you'd only be kidding yourself if you read the asnwer then answered it! Anyway, can you change my answer??? I got it wrong because I didn't know the meaning of the word adjacent! So technically I am stupid, but it wasn't my mathematical skills that let me down - I have lots of paper with revolver chambers drawn on them here on my desk to prove it!!!

Now here is another question for you - 2 revolvers, 1 has 2 bullets in adjacent chambers, one has 2 bullets in opposite chambers. Both randomly spun, you have to pick one to fire at your head. Which one and why? Probability is the same but if you HAD to pick one which would it be and what is your thinking for doing so....

Sam.