Puzzleing Question! (HARD) - Page 57

On November 24 2004 14:32 Catyoul wrote:
Elaborate, you're just reformulating : "no no no, you are wrong."

Let's take the statistical approach with big numbers, which will tend to the correct probability. So we have our 1000 houses again. Let's say you are going to knock on all doors, because that's what you do to get the probability for all the cases.

What happens at the 3 different type of houses :
- The girl / girl houses : a girl answer the door. ALWAYS. That makes 250 houses with a girl always answering
- The girl / boy houses : a girl answer the door, 1/2 the time. That makes 500/2 = 250 houses with a girl answering and 250 with a boy answering
- The boy / boy houses : a boy answers the door, always. That makes 250 houses with a boy answering.

Totals : 500 houses with a girl answering, 500 with a boy answering... of course !

Now the problem tells us, as you underline, that a girl opens the door. So we are in the 500 cases where a girl has opened the door. In those 500 cases, we see that 250 come from girl/girl houses and 250 from girl/boy houses. That makes 1/2 for the second child to be a boy and 1/2 for the second child to be a girl.

Let's see if we agree on basic probabilities just to be sure.

1. I show you the first 9 flips, they happen to be tails. What's the probability for the 10th one ?
2. I tell you there are at least 9 tails. What's the probability for the 10th one (the one that isn't included in the 9 tails I told you) ?

If you don't understand how these 2 questions are different, sorry I can't say much more.

3rd question, more tricky
3. I tell you there are at least 9 tails. Now, what's the probability of the flip number 10 (not the 10th one like in question 2) to be head or tail ?

Btw, the correct answers are :
1. 50% tail 50% head
2. 1/11= ~9% tail 10/11 = ~91% head
3. 10/11 tails, 1/11 heads

On November 24 2004 14:43 Catyoul wrote:
(7+1/7)*(7+7) = 100

On November 24 2004 15:20 Catyoul wrote:
Although I find your idea a bit far-fetched