Scratch off

Here is another company promotion. A local car dealership sent out a flyer with scratch-offs. People can't resist scratch-offs, so that is a bit of a ploy in itself.

You can win:

• $25,000        Odds        1:25,000
• $500             Odds        1:25,000
• $2                 Odds        24,996:25,000     OR     $25,000        Odds        1:25,000
• $1,000          Odd          1:25,000

I know that third line looks a little funky, but that is how they had it in the ad. The connector between all of these are "or" so what is the point? I guess they're trying mess with your head again and make it look more likely that you will win something other than the $2 prize. (We'll give them a pass on the fact that these are actually probabilities and not odds.)

To the casual observer it looks like a pretty good chance of making a lot of money - either a 3 out of 4 or a 4 out of 5 chance. Of course, in actuality, the chance of getting anything good is 4 out of 25,000 = 0.016%.

So students could do a number of things to analyze this psychologically and mathematically. Another activity is to find the expected value:

0.00016 x $25,000 + 0.00016 x $500 + 0.00016 x $25,000 + 0.99984 x $2 +  0.00016 x $1,000
= $10.24

So, I guess there is no harm in trying for it. I did the scratching. It gave a code and then you had to call to see what you won. I'm sure this gives them another chance to talk you into buying a car - and to give you, undoubtedly, your $2.

My preference - If I do by a car, save the promotion and just take $10.24 off the price.