Win a Goat!

You find yourself in an empty room, and in the adjacent room there are a bunch of people.
One person will come over from that room to your room. What is the chance that he/she's a female?


50%


Well now I tell you that in fact, there's a men's football (soccer) starter team and a women's basketball starter team in the other room. That gives you 11 men and 5 women. What's your chance of getting a woman now?


31.25%


Notice how nothing changed between the first and the second part - no one moved, no one exited, entered, teleported - nothing is physically different! Your odds changed from one moment to the other, simply because of the information you possessed.
The women's basketball team is actually a wheelchair basketball team, and they left their wheelchairs at home:


0%


Again. Same room, same people as before but your chances are so different!

A probability is only as good as the extent of information you have about the problem... and it changes over time! The more you know, the more it changes.

Check out this cool problem posed in 1975 (The Monty Hall problem):
You arrived to the final stage of a television game show. You have a choice between three doors: behind one is a brand new car, behind the other two there are goats. You get to take home whichever one you choose.

So you courageously choose one.

But here's the twist: Monty Hall, the host of the show, opens one of the two doors that you didn't pick (he opens one with a goat in it) AND he gives you a chance to change your choice to another door?

Now you can choose between two doors; one has a goat behind it and one has a brand new car. Do you switch to the other door?


I will post about the right choice in a few days... until then, think about it!


(By the way a really really cool commercial about wheelchair basketball: http://www.youtube.com/watch?v=xwndLOKQTDs )