# A riddle my brother gave me today

by bohm 101 Replies latest jw friends

• ##### bohm

A man has 2 children. He tells you one is a boy born on a tuesday. What is the probability the other is a boy to?

(with the loosest assumptions, ie. we assume a-priori there is a 1/2 chance to give birth to a boy independent of past births, no twins, and no more boys or babies are born on tuesdays than other days of the week (on average)).

Its not very hard, but it show how hard it can be to combine information - quickly, is the probability highter than, lower than or equal to 1/2?

• ##### John Doe

The probability of one child being a boy is 1/2. The probability of two childs being boys is 1/2 x 1/2, or 1/4. However, since we know that one child is a boy, that only leaves us with the probability of one child being a boy. So, the answer is 1/2.

• ##### snowbird
The probability of two childs being boys is 1/2 x 1/2, or 1/4.

What Doe said, minus the childs.

Syl

• ##### Albert Einstein

Hi Bohm,

its lower than 1/2.

If it is a boy, it would be just 1/2.

But if it is a boy, he must be born any other day than Tuesday so it only gives 6/7 chance (There already is one born on Tuesday ...)

Albert

• ##### John Doe
But if it is a boy, he must be born any other day than Tuesday so it only gives 6/7 chance (There already is one born on Tuesday ...)

Nothing in the story supports that the other child must be born on a day other than Tuesday. And, even if that were stipulated, it would have no bearing on the sex of the other child. That's merely superfluous information to distract you.

• ##### bohm

Albert is right - its lower than 1/2.

Good to see you again Albert! i hope everything is cool with you wife.

JD - thats not quite right. Try this example: A man has 20 children. He tells you 19 are boys. What is the probability the last one of them is a boy to?

• ##### John Doe
Albert is right - its lower than 1/2.

You're going to have to give an explanation. As your puzzle stands, I can see no way of construing that as less than 1/2.

• ##### John Doe
JD - thats not quite right. Try this example: A man has 20 children. He tells you 19 are boys. What is the probability the last one of them is a boy to?

1/2.

• ##### changeling

The more you have of one gender the better the chances of having more of the same... It increases exponentially...I think...

• ##### changeling

The Tuesday detail is irrelevant...