A woman has two children, at least one of which is a boy...

[Chowlett]

Originally posted by Rogan Josh
Is it just me or is all this bloody obvious? (Clearly not - since there is so much debate....)

It's bloody obvious, but only if you have some training in it first. We as a species are notoriously bad at probability - possibly because evolutionarily speaking, we had no need to improve. A distinction into "Never", "Unlikely", "Possible", "Likely" and "Certain" is probably all we ever really needed to survive.

As an example, without doing any calculations (and shh if you know the answer already), take a ballpark guess at the following questions.

1) How many people do you need before the probability that at least two share a birthday is greater than 1/2 (ie, when does it become more likely for there to be a coincidence than not)?

2) How many people do you need before the probaility that at least one of them has your birthday is greater than 1/2?

I know the answer to the first by heart, and I know the second one roughly. I'll work it out and post after a few people have had a go. But don't post your reasoning, or do detailed calculations - this is about intuition.

Guesser	First Problem	Second Problem
Victor Gallis	184	730
Boddington's	27	183
Rah	25	183
Richard Burns	19	182
SD	25	250
Paul	20	183
Adam Smith	20	183
Dr. Oogkloot	-	260
Wernazuma	19	183

[Immortal Wombat]

Originally posted by Chowlett

As an example, without doing any calculations (and shh if you know the answer already), take a ballpark guess at the following questions.

1) How many people do you need before the probability that at least two share a birthday is greater than 1/2 (ie, when does it become more likely for there to be a coincidence than not)?

2) How many people do you need before the probaility that at least one of them has your birthday is greater than 1/2?

Hehe

I know the answer to the first by heart, and I know the second one roughly. I'll work it out and post after a few people have had a go. But don't post your reasoning, or do detailed calculations - this is about intuition.

I know the first one, but not the second.

[Rogan Josh]

Originally posted by Chowlett
1) How many people do you need before the probability that at least two share a birthday is greater than 1/2 (ie, when does it become more likely for there to be a coincidence than not)?

2) How many people do you need before the probaility that at least one of them has your birthday is greater than 1/2?

I know the answer to both of these (don't worry - I will keep quiet ) although I must confess I used my calculator for the first one.

Interestingly though, I tried guessing the first one before working it out (the second one requires no calculation) and was quite a bit out (although surprisingly, I was too low with my guess....).

Edit: I take that back for question 2. I misread it

[Chowlett]

Originally posted by Rogan Josh

(the second one requires no calculation)

You sure? PM me your answer.

[Victor Galis]

To those who still don't believe Krazy and Jon, I propose a wager. We'll survey 100 women who have exactly two children, including at least one boy. (Shouldn't be hard to set that up in an online chat room or something.) If at least 51 of them have a girl in addition to the boy, you pay me $1000. If not--if at least 50 of them have two boys--I'll pay you $1500. If Harrison is right and I'm wrong, I'm offering you 3/2 odds on a 50-50 bet. Any takers?

-That's an entirely different problem from that which I suggested that the answer is 1/2. (see my second or third post where I came up with 1/3)

If the question is:

A woman has two children, (the first or the second) of them is a boy, what is the chance that the other is a boy?
The answer is 1/2.

If the question, is we find a population of women with 2 children, at least one boy, then the probability of randomly selecting one that is has another boy is 1/3.

"1) How many people do you need before the probability that at least two share a birthday is greater than 1/2 (ie, when does it become more likely for there to be a coincidence than not)?"

183.125

"2) How many people do you need before the probaility that at least one of them has your birthday is greater than 1/2?"

Hmmm... I'd say 730.5 including yourself. These are rough guesses made between classes.

[Chowlett]

I'm now keeping a tally. To clarify things, I'm only considering integer numbers of people, so round up your guesses. I'm also not counting you in the second problem. And just to make things easier, all years are assumed to have 365 days, and birthdays are assumed to be evenly distributed throughout the year (fallacious, but hey)

[rah]

rough guesses

1. 20-30 people
2. 183

RAH

[Provost Harrison]

OK, OK, let me get my calculator

[Provost Harrison]

Originally posted by Victor Galis


-That's an entirely different problem from that which I suggested that the answer is 1/2. (see my second or third post where I came up with 1/3)

If the question is:

A woman has two children, (the first or the second) of them is a boy, what is the chance that the other is a boy?
The answer is 1/2.

If the question, is we find a population of women with 2 children, at least one boy, then the probability of randomly selecting one that is has another boy is 1/3.

I think Victor has a point and this is coming down to an issue of semantics in the question itself. I can certainly see where 1/3 has come from. Let's face it, the wording of the question is ambiguous.

[Richard Bruns]

Originally posted by Chowlett
As an example, without doing any calculations (and shh if you know the answer already), take a ballpark guess at the following questions.

1) How many people do you need before the probability that at least two share a birthday is greater than 1/2 (ie, when does it become more likely for there to be a coincidence than not)?

2) How many people do you need before the probaility that at least one of them has your birthday is greater than 1/2?

I know the answer to the first by heart, and I know the second one roughly. I'll work it out and post after a few people have had a go. But don't post your reasoning, or do detailed calculations - this is about intuition.

I haven't looked at anything after this post and I only took a basic statistics course, so I'll take a few blind guesses:

1: about 19, or whatever the square root of 365 is.
2: 182

edit: messed up quote tag

[Dauphin]

Problem 1: ~25
Problem 2: ~250

[Paul]

Problem 1: 20
Problem 2: 183

[Ramo]

Edit: I wasn't supposed to put down the answers, eh? Ermm.. my bad..

[Dauphin]

Edit that out.

So much for the no calculations rules. You were supposed to estimate on face value!

[Dauphin]

Its all well and good being able to calculate the answer, but you won't get far if you don't read the rubric.