**Next message:**Eliezer S. Yudkowsky: "Re: Microsoft Is Set to Be Top Foe of Free Code"**Previous message:**Bryan Moss: "Re: Microsoft Is Set to Be Top Foe of Free Code"**In reply to:**Zero Powers: "Re: Keeping AI at bay (was: How to help create a singularity)"**Next in thread:**Amara Graps: "re:Fun with Bayes' Theorem"**Maybe reply:**Amara Graps: "re:Fun with Bayes' Theorem"**Reply:**scerir: "Re: Fun with Bayes' Theorem"**Reply:**Adrian Tymes: "Re: Fun with Bayes' Theorem"**Reply:**Lee Corbin: "Re: Fun with Bayes' Theorem (Answers)"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

You don't really need to know that

P(Ai|B) = [P(Ai)P(B|Ai)]/P(B)

(it probably doesn't help). But it certainly helps to

consult your imagination for the following problems.

1. There are two bags, each with 10 coins. Half the coins

in the first bag are counterfeit, and all the coins in

the second bag are counterfeit. Someone hands you a bag,

and you happen to pull a coin out of that bag and examine

it. If you see that the coin is counterfeit, what is the

probability that you were handed the counterfeit bag?

2. A little girl's father discovers that his wife is

pregnant again (but they don't know the sex of the

unborn child). The man decides to visit a mathematician.

"I have two children, sir", he says, "and one of them

is a girl. What is the probability that the other is

a boy?" What did the mathematician tell him?

3. You're on the Monte Hall show, and there is a big prize

behind one curtain, and junk prizes behind the other two

curtains. You pick one of the three at random. Monte

then opens one of the other curtains and shows you a

junk prize, and asks if you still want to keep playing.

You say, "Yes, but let me switch my choice to the other

curtain!". Monte says, "That's weird," but allows the

switch. What is the probability of your getting the big

prize? (As is widely known, Marilyn Vos Savant humiliated

some experienced mathematicians with this old problem.)

4. You wash up on a desert island where it is known that Long

John Silver has hid a lot of gold in one of three strongly

built shacks. You begin dismantling one of the three. A

lightning bolt comes out of the overcast sky and strikes

one of the other shacks, destroying it and revealing that

the gold wasn't there. What is the probability that the

gold will turn up in the shack that you are not working on?

Hint: one of the answers is 1/2 and the others have the same

answer.

Lee Corbin

**Next message:**Eliezer S. Yudkowsky: "Re: Microsoft Is Set to Be Top Foe of Free Code"**Previous message:**Bryan Moss: "Re: Microsoft Is Set to Be Top Foe of Free Code"**In reply to:**Zero Powers: "Re: Keeping AI at bay (was: How to help create a singularity)"**Next in thread:**Amara Graps: "re:Fun with Bayes' Theorem"**Maybe reply:**Amara Graps: "re:Fun with Bayes' Theorem"**Reply:**scerir: "Re: Fun with Bayes' Theorem"**Reply:**Adrian Tymes: "Re: Fun with Bayes' Theorem"**Reply:**Lee Corbin: "Re: Fun with Bayes' Theorem (Answers)"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

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