# Dan: Simple probability questions

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Dan: Simple probability questions

Jack is playing cards with his friends. He deals 1 facedown card to each player. Player A announces he thinks he has the queen of diamonds.

Q1: What is the probability Player A has the queen of diamonds?

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97%?

Almost sprayed my coffee on that one!

How many cards? 32? 54?

It depends of the sorting too, who gets the first card sorted. Or am i just making it more complex for nothing?

Assuming no jack card, 1/52. What is your point?

Right. Player B thinks Player A has the queen of spades. Player C thinks Player A has the queen of hearts. Player D thinks Player A has the queen of clubs.

Q2: What is the probability player A has the queen of spades?

Q3: What is the probability player A has the queen of hearts?

Q4: What is the probability player A has the queen of clubs?

This should be interesting

1/52
1/52

Q5: What is the probability Player A has a queen?

1/13

During the card game, Jack notices his son Joe has not come home from school yet. Player A thinks Joe is at Tom's house.

Q6: What is the probability Joe is at Tom's house?

Not enough information.

Depends on the credibility of the evidence of person A. For example if its mum, maybe its quite high.

Joe is either at Tom's house or not at Tom's house (it's boolean). You told us that repeatedly that in such a case it should be 50%. So again:

Q6: What is the probability Joe is at Tom's house?

No thats not a boolean question. There are many place Joe could be other than Tom's house.

Joe is either at Tom's house, or not at Tom's house. That is boolean.

Q6: What is the probability Joe is at Tom's house?

There is in built evidence in the question; we know there are more than two possible place Joe could be so we know its not a boolean question. Boolean questions have two possible outcomes. Your question has more than two possible outcomes so its not boolean.

Dan - Your question has more than two possible outcomes so its not boolean.

My question only has two possible outcomes:

• Joe is at Tom's house.
• Joe is NOT at Tom's house.

Q6: What is the probability Joe is at Tom's house?

So to put it this way, there could be a 1000 houses that Joe could be at; so the probability is 1/000. So your question in not over a boolean sample space it is over a sample space of 1000 so not a boolean question at all

@Dan

Dude, it ain't rocket science. Either Joe is at home, or he is somewhere else. Does not make a hoot nor a holler where that "somewhere else" might be. Joe is either home or not at home. Period. Hell, even my rusted old brain bucket can understand that. Sheesh....

You need to read the other thread with the questions on probability.

In short, the underlying sample space for the question 'is joe at home' is not boolean as there are more than 2 places Joe could be, so the answer space is not a normal distribution.

In contrast if you consider the question 'is there a creator god?' the sample space is boolean and so it has a normal distribution

This is hilarious. Nyarl presented two possibilities, they are logical negations of each other, and the scenarios you're offering are all encompassed in one of those possibilities. Dear oh dear...

"Boolean, or boolean logic, is a subset of algebra used for creating true/false statements. Boolean expressions use the operators AND, OR, XOR, and NOT to compare values and return a true or false result."

Nobody mention Schrodinger's cat ffs, or I may start self harming.

I think it is quite telling that you repeatedly claimed this "rule" was valid only a few hours ago, when it gave you the results you wanted; but won't apply it now that you know it is going to blow up in your face. It is special pleading.

Also your suggestion that the question isn't boolean, is just silly.

@Dan

Would it help if Nyarlathotep rephrased the question to make it "boolean" enough for you? The point of his question was not to trick you with wording on the question with hypotheticals but to point out how statistics works.

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It's funny how Dan tap dances around a simple boolean question. Nyarl's question has only two answers.
Either Joe is at Tom's house, or not a Tom's house.

Well to finish the story for anyone who is interested:

We'll find using Dan's "logic" that there is:

1. 50% chance Joe is at Tom's house.
2. 50% chance Joe is at Sue's house.
3. 50% chance Joe is at Jill's house.
4. 50% chance Joe is at Ann's house.

Leading to the very dubious conclusion that there is a 150% chance that Joe is at a girl's house.

@Nyar Re: "Leading to the very dubious conclusion that there is a 150% chance that Joe is at a girl's house."

Well, you know what they say about good ol' Joe. He's a player.

"Leading to the very dubious conclusion that there is a 150% chance that Joe is at a girl's house."

I'm 150% ok with that.

No because the sample space for all those questions is not boolean... You guys are being deliberately obtuse I think...

Wen't back and read the posts. I thought it was a riddle and I was missing something. Awesome Point Made!!!!

'Will I get a 6 when I toss a dice'

The question is boolean, but the underlying sample space is size 6 for this question.

In your question, the underlying sample space is the number of houses, IE 1000s, Joe could be at.

So neither question has a boolean sample space.

The question 'is there a god' has a boolean sample space so 50%/50% is the correct starting point.

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