Fun with Numbers

I know there are people who hate math.  I see their posts on Facebook.  And some talk about how story problems are, to them, incomprehensible.  To which I say, "Life is a story problem."  In engineering, every problem is a story problem. 

I don't understand not liking math because I do like math.  I don't really love it because I'm not really good at it.  I'm slow and have to think a lot.  I took math in college up through differential equations which I loved because it took all that math (algebra, calculus, etc.) and applied it to the real world.  If someone asks me why they have to study algebra I say (if I'm feeling snarky), "So you can study calculus and God speaks calculus."

It's been 20 years since I graduated college (almost) and because I haven't used my calculus and differential equations, I've pretty much forgotten how to do them.  I know the principles involved, but to sit down and do a derivative or an integral, forget it!  But I still enjoy math.

One area of math were a lot of people have misconceptions is statistics.  That is probably because there's "luck" involved, they think.  You've heard, perhaps, that the lottery is tax on those bad at math?  Well, specifically, it's a tax on those bad at statistics.  According to the Powerball page the odds of winning the big prize are 1 in 175,000,000.  That's one ticket out of 175,000,000.  The odds of flipping a coin and getting heads is 50% (1/2).  The odds of winning the Powerball is 0.0000000057% (1/175,000,000).  That's close enough to zero to basically be zero.

The odds of being hit by lightning sometime in your life is 1 in 3,000.  So you are 58,333 times more likely to be hit by lightning in your lifetime than to win the Powerball lottery with one ticket.  Or, to make the odds of being hit by lightning the same as winning the Powerball, you'd need to buy 58,333 tickets in your lifetime.

So don't play the lottery.

Powerball is different for a lot of lotteries because of the power ball.  But if a lottery is where you pick six numbers out of, oh, 50, then any six numbers have the same (low) odds of winning.  Using 1, 2, 3, 4, 5, 6 will win just as much as any other six-number combination (including your grandchildren's ages).  It doesn't matter which numbers you play, you'll still lose.

Another area people don't understand statistics is with lucky runs.  The odds of flipping a coin and getting heads is 50% (1/2).  The odds of doing that three times in a row is 12.5% (1/2 x 1/2 x 1/2).  That means if you flip a coin three times 1,000 times, 125 times you'll get three heads in a row (or three tails).  So on that fourth throw, what are the odds of getting a heads?  It's 50%. Coins don't have memory.  Before the first flip the odds of flipping a coin and getting heads four times is 6.25%.  But after three flips (all heads) the odds the next flip will be heads is 50%.  Most people don't believe that (bar bet time!).