6.29.2010

Probably

This is why I fared so poorly in Probability class in college.

Let's say I flip two coins.  I call you up on the phone and say, "Hey, I just flipped two coins and one of them is heads."  Guess what the odds are that the other coin is heads.

Did you say 50%?  Nope.  Turns out the odds are 1 in 3.  Here's the breakdown: if I flip 2 coins, there are four equal possibilities:

• heads / heads
• heads / tails
• tails / heads
• tails / tails

Now,when I tell you one of the coins is heads, the last possibility no longer is possible.  That leaves three possibilities, two of which have the other coin being tails.  So, the odds of a heads is one in three.

Now, let's say I call you up again and tell you, "Hey, I just flipped two coins and the one in my right hand is heads."  What are the odds the other is heads?

Did you say 1 in 3?  Sorry.  It's 50%.  Looking at our chart again, if I say one particular coin is heads, that eliminates two of the possibilities (where that coin is tails), leaving only two possibilities, of which only one has the remaining coin being heads.

That means, if I asked you the first question, and you said, "Which one?"  If I answer, regardless of the answer, the odds of you getting the right answer go from 1 in 3 to 1 in 2.

What exactly does this mean?

This means that probability is harder than it looks.  So if you see people casually tossing around probabilities, percentages and other numbers, trying to make a point, know that the math may not actually be that easy and be sure to think twice about it.

(The Two Sons Problem)

posted by risser at 12:00