Puzzle time - who’s bullet?

[Horace]

@taiwan_girl said in Puzzle time - who’s bullet?:

@jon-nyc #1 and #2 cannot happen. In the riddle, one bullet hits you said. I think that leaves only 3 and 4

Yes good job TG. So regardless of what the absolute probabilities of 3 and 4 are, the puzzle is to determine the ratio between the two.

[taiwan_girl]

I will think some more. Should not be too difficult. Lol

[Doctor Phibes]

||spoiler||
Both hit - chance is .75 x .25 = .1875
Both miss - chance is .25 x .75 = .1875
J hit, K miss - chance is .75 x .75 = .5625
J miss, K hit - chance is .25 x .25 = .0625

If one bullet hits, either case 3 or 4 has taken place. Chance it was Jon is .5625/(.5625+.0625) = 90%.

[taiwan_girl]

@Doctor-Phibes your spoiler didn’t work. LOL

but what you did makes sense. I am going to claim that I would have done the same answer.

[Doctor Phibes]

Bugger, sorry.

[brenda]

@Doctor-Phibes said in Puzzle time - who’s bullet?:

Bugger, sorry.

Don't be sorry. You are t3h stats jock!

[jon-nyc]

@taiwan_girl said in Puzzle time - who’s bullet?:

@jon-nyc #1 and #2 cannot happen. In the riddle, one bullet hits you said. I think that leaves only 3 and 4

Well it’s an intermediate step which allows you to get to the conditional probability that the target is hit by only one bullet.

[jon-nyc]

To make the problem more realistic instead of shooting a target the puzzle should have been successfully playing a Rachmaninoff etude.

[taiwan_girl]

@jon-nyc

[Mik]

Neither one. Klaus can't shoot and you're drunk.

[Doctor Phibes]

What's the probability of somebody's family member shooting either Klaus or Jon as they attempt to play a Rachmaninoff etude?

[Klaus]

Exact Bayesian inference for the win.

normalize $ do
    k <- coin 0.25
    j <- coin 0.75
    if ((k && not j) || (j && not k)) then (if k then return "Klaus" else return "Jon") else fail

Result:

Dist [(0.9,"Jon"),(0.1,"Klaus")]

[Doctor Phibes]

Fucking IT people.

[Horace]

@Doctor-Phibes said in Puzzle time - who’s bullet?:

Fucking IT people.

Not in this lifetime. Nerds.

[Klaus]

I have a similar puzzle for Jon.

Jon sends us a recording of a Rachmaninoff etude and tells us that it is a recording from him.

Jon is a trustworthy forum member, so before listening we are 99% confident that Jon tells the truth and didn't actually send us a recording by Klaus (which would be flawless).

However, we also know that the probability that Jon hits a correct note is only 40%.

We start listening to the 10 first notes. They are all correct.

What's the likelihood that it is indeed Jon's recording?

[jon-nyc]

100.0%