Thursday, November 29, 2012

Powerball Odds

As my daughters get older, I hope to impart upon them a bit of wisdom regarding simple statistics.  If you live in the United States you are probably well aware that the largest Powerball lottery drawing in history took place last night.

Before the drawing, the lottery reached almost $580 million.  This morning I was checking out various news sources to see if anybody had won.  It turns out there were 2 winning lottery tickets sold.  The odds of winning the biggest prize are 1 in 175 million, so not very good.  Your odds of getting struck by lightning are better than this.  The same article goes on to state, however, that your odds of winning something in the Powerball lottery are "pretty good".  I put "pretty good" in quotes, because those are the exact words the article used.  So the question is, what is "pretty good"?  The odds of winning anything in the Powerball lottery are 1 in 32.  Pretty good?  Hardly.  Granted, 1 in 32 is much better than 1 in 175 million, but let's not kid ourselves.  A 1 in 32 chance is not "pretty good".  Switching over to percentages, a 1 in 32 chance means you have a 3.1% chance of winning something.  

Let me put this in a different perspective.  Let's say you go to the doctor and the doctor tells you that you have a potentially deadly disease (i.e. cancer).  Let's also say the doctor goes on to tell you that you have a 3.1% chance of surviving this disease.  Are you going to be happy with that chance?  I doubt it.  A very optimistic person will say that there's a chance they can survive which is better than no chance, but the average person is going to look at that and realize they are likely to die.  If I'm in that position, I'm going to remain hopeful, but at the same time I'll be getting my affairs in order to make sure my family is prepared in the statistical likelihood that I won't make it. 

To conclude, odds of 1 in 32 are NOT "pretty good".

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