Maths problems (interesting ones)

[FizMan]

I think you're off Kris... I'm going to trust my highschool Finite math on this one...


We'll do it your way:


Door Opener / Non Door opener

Boy / Girl
Boy / Boy

Girl / Girl
Girl / Boy


Okay, a girl opens the door... so you say that eliminates the first two possibilities...

Why? Remember, two combinations of boy/girl exist, and you've eliminated one of them for the wrong reason.

Whoever opens the door does not determine what children exist in the family (with the exception of the boy/boy possibility)

If you want to keep your method of reasoning, we have to add more possibilities. That is, the order of children. I'll mention the first born child, the other is safely assumed to be the second born:


Door Opener / Non Door opener

Boy (1st born) / Girl
Boy (1st born)/ Boy

Boy / Girl (1st born)
Boy / Boy (1st born)

Girl (1st born)/ Girl
Girl (1st born)/ Boy

Girl / Girl (1st born)
Girl / Boy (1st born)


Eliminate the Boys answering the door, you're left with the last four. We can eliminate one of the extraneous Girl/Girl possibilities as well.

Girl (1st born)/ Boy

Girl / Girl (1st born)
Girl / Boy (1st born)

Voila, 1/3.

[mtrawls]

Okay. I, too, have heard those before, so I'll propose my own (well, as you might guess, it is by no means original with me). Suppose that there is a game where we flip a coin. If the first time the coin is flipped it lands on heads, I pay you $2 (2^1), if the first time it lands on heads is the second toss, I pay you $4 (2^2), if the first time it lands on heads is the third toss, I pay you $8 (2^3), ad infinitum. Using simple probability, tell me how much you would pay me to play this game and still be able to make a decent profit (but enough to tempt me to agree to the game).

[FizMan]

You mean, for example, if I said, "Hey mtrawls, I'll pay you $20 to play <insert above mentioned game here> with me"?

[mtrawls]

Originally Posted by FizMan

You mean, for example, if I said, "Hey mtrawls, I'll pay you $20 to play <insert above mentioned game here> with me"?

Exactly. And for those interested in finding the answer without doing the math (shock! pure blasphemy, I daresay), try searching for the St. Petersburg Paradox from our good friend Bernoulli (ah, but which one?)