Logic Puzzles

A place for people to post puzzles to confuse and confound, then impress everyone with your amazing powers of reasoning and deduciton.

Post up your puzzle without an answer, hopefully someone will be able to provide an answer and the reasoning behind it.

First up, an easier one: A lady has two children. One is a boy. What are the chances of the other child also being a boy?

Remember to post your reasoning behind the answer, and no cheating!

Riddle me that

'A lady has two children. One is a boy. What are the chances of the other child also being a boy?"

Zero - you've just said one is a boy.

Assuming the probability of having a boy or girl is 50% then the options are:

BB, GB, BG so 1/3?

Ah, I suppose you're technically correct although that wasn't the answer I was looking for. Let me re-word the question slightly:

A lady has two children, of which we know at least one is a boy. What are the chances of the other child also being a boy?

Too slow, Trunkie has it.

Riddle me that
Those pesky bees!

Or her mum with a sore throat.

'A lady has two children. One is a boy. What are the chances of the other child also being a boy?"

Zero - you've just said one is a boy.

This.

Here's a famous one (don't spoil it if you're familiar with it) along the same lines:

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

Should I subscribe to this thread or not?

iswydt

Too slow, Trunkie has it.

[strike]Why is it not 50% as GB gives the same result as BG?

The fact that one child is a boy has not bearing on the sex of the second child.

Maybe I'm missing something in the way the question is worded?[/strike]

Got it now.

2 nuns in a bath

one says 'where's the soap?'

where is the soap?

Why is it not 50% as GB gives the same result as BG?

The fact that one child is a boy has not bearing on the sex of the second child.

Maybe I'm missing something in the way the question is worded?

I thought the same - so looked this up (https://en.wikipedia.org/wiki/Boy_or_Girl_paradox )- there's a section that explains the ambiguity of the question. i.e. did they look for that family with two kids, at least one of which was a boy to ask the question about (in which case pr = 1/3) or or did they choose a random family and then make a statement about the kids in it (in which case pr =1/2).

At least I think that's what it says...

I thought the same - so looked this up (https://en.wikipedia.org/wiki/Boy_or_Girl_paradox )- there's a section that explains the ambiguity of the question. i.e. did they look for that family with two kids, at least one of which was a boy to ask the question about (in which case pr = 1/3) or or did they choose a random family and then make a statement about the kids in it (in which case pr =1/2).

At least I think that's what it says...

Question says:
"mother has at least 1 boy..."
So GG is not possible, leaving 3 possibilities, BG, GB, BB.

"Out of those possibilities, what's the probability both kids are boys":

1/3

Question says:
"mother has at least 1 boy..."
So GG is not possible, leaving 3 possibilities, BG, GB, BB.

"Out of those possibilities, what's the probability both kids are boys":

1/3

Yes, I agree. But, to remove the ambiguity, the question could say 'from a sample of famillies with at least one boy', in which case there are only three possible possibilities.

On the other hand, if you think that a family was chosen at random (so GG is possible) and then a question asked about that question which happened to contain at least one boy then the answer is 1/2 I think

2 nuns in a bath

one says 'where's the soap?'

where is the soap?

Yes it does.

Yes, I agree. But, to remove the ambiguity, shouldn't the question say 'from a sample of famillies with at least one boy', in which case there are only three possible possibilities.

On the other hand, if you think that a family was chosen at random (so GG is possible) and then a question asked about that question which happened to contain at least one boy then the answer is different I think

Ardicius rephrased the question to be:

A lady has two children, of which we know at least one is a boy. What are the chances of the other child also being a boy?

"of which we know at least one is a boy" limits the possibilities to the sample of families with at least one boy.

Ardicius rephrased the question to be:

"of which we know at least one is a boy" limits the possibilities to the sample of families with at least one boy.

I don't think we can tell from that statement whether the family was chosen from a sample of families containing 2 children of which one was a boy (1/3) or if the family was chosen from a sample of families containing 2 children (and the statement about the sex was made afterwards based on that choice) (1/2).

I just read that wiki page. [strike]Fuck logic. :)[/strike]

It's pretty interesting the stuff they're talking about, about how people estimate probabilities. Intuitively, the probability that a child is a boy is 1/2, regardless of any other children.

Maybe this is how the Monty Hall problem (a whole other kettle of fish) confuses people.

Drakien has the right logic behind this one. I instinctively thought the answer would be 1 in 2, because you know the first child is a boy, it has no bearing on the sex of the second child and the chances of a child being a boy or being a girl are both (for the sake of simplicity) 1 in 2. But there is a flaw in the logic here because we are assuming that the one child we know the sex of has been assumed to be the first (or second, it doesn't matter).

Therefore we have to look at all possible combinations (BB, BG, GB, GG) and see how likely it is that the desired outcome would occur. We can discount GG because we know at least one is a boy. Leaving 3 possible outcomes, with only 1 being the desired result, therefore 1 in 3.

Actually, that's a pretty interesting wiki page. My whole thread is ruined!

if it takes a week to walk a fortnight, how many apples in a barrel of grapes?

A bat and ball cost $1.10.

The bat costs one dollar more than the ball.

How much does the ball cost?

Mu^