A riddle my brother gave me today (page 5)

TheSilence

50% give me a minute and I will explain it a little more clearly if I can.

The probability of 2 things being something is the probability of 1 times the probability of the other... so if you have 2 children and you don't know the gender of either the probability of both is 1 in 4. 1/2 * 1/2.

However, in the scenario you provided we already know the gender of one of the children as being a boy. So the probability of *that* child being a boy is 1/1 because we already know. So the probability of both children being boys becomes 1/1 * 1/2 = 1/2 or 50%.

Already knowing the gender of one child effects the equation and the probability, and most people fall into the trap of thinking it doesn't have any effect on the numbers at all. In the scenario you provided there is a 1 in 2 shot of the unknown child being a boy. A 50/50 chance. 50%. I hope that makes sense.

Jackie

bohm

Jackie:

However, in the scenario you provided we already know the gender of one of the children as being a boy. So the probability of *that* child being a boy is 1/1 because we already know. So the probability of both children being boys becomes 1/1 * 1/2 = 1/2 or 50%.

The last conclusion is false, since when you know at least one is a boy the two events are no longer independent, thus you cannot multiply the probabilities.

Hint: No advanced stuff needed to solve the problem besides counting.

TheSilence

:::chuckling::: I would stay and debate with you, but I'm leaving for work. Let me leave you with this: I majored in math and took many statistics and probabilities classes. In addition, I work in a casino where every day I work with probabilities. You can believe whatever you will, but my answer is correct. Ask a statistics professor and I would bet you that he gives you the same answer that I did.

Jackie

bohm

Jackie: Bring it on girl, i got a drivers licence for a seewing-machine at my school!

Nevertheless its NOT 1/2. Since you work with gambling, do you want to bet a beer? (im serious, i will type my calculation and send you the money if it is found to be incorrect).

crapola

I totally am confused as to what this is all about but it's also late and I took my sleeping pill already,soooo, maybe that's why I'm in lala land.

StAnn

The other child is a boy. The father is distinguishing between the boys by telling you that he has one boy born on a Tuesday and another boy born on another day.

Hey, it's as good a guess as the rest.

It's actually 13/27.

StAnn

bohm

crapola - its just a riddle that got mixed up in a discussion by me and John Doe.

StAnn.: Its not a trick question.

Duncan

Hi bohm and everyone

This is actually, in maths circles, a very famous and fairly old riddle. My son (currently doing a Master's in Maths at Cambridge) e-mailed this riddle to me earlier this year. It's not just a maths problem - it's also involves semantics.

Wikipedia has an excellent article on it:

http://en.wikipedia.org/wiki/Boy_or_Girl_paradox

It's a fairly long and difficult article to plough through - and I'm not even going to attempt to summarise it - but take a look if you're interested in why the answer is not necessarily just 50%.

Duncan.

dozy

Semantics aside , the odds are slightly higher than 50%. Approx 105 boys are born to every 100 girls - much higher in China & other countries.

A riddle my brother gave me today

Share this