Expected Value

The topic this week in Probability was Expected Value. Unlike many of the topics, which I have been exposed to before, this one was completely new to me.

It is such a useful idea! If McDonald's has 5 different Happy Meal toys (do they still do that? Or do unhealthy foods advertising to kids not allow it anymore?), and there is an equally likely chance you will get any one toy, how many should you expect to buy to get them all? The answer is about 12. Now, you may be lucky and get them in just 5 purchases, or you may get unlucky, and have it take many many more than that, but on average (say you and 1,000 of your closest friends are all collecting the toys) it should only take 12 purchases.

One of my favorite things to do at a store is buy a grab bag. If you know 20% of the grab bags are worth $100, and 30% are worth $50, and 50% are worth $10, is it a good idea to pay $25 to choose one at random? Expected value can help you inform your decision. On average, the return of a grab bag is $40, so paying $25 is a reasonable gamble.

Probability classes are generally a lot of coin flipping and dice rolling, so the real life application of expected value was what really made me interested in my topic. On a phone call with my Dad, who works in finance, I mentioned the topic we were covering, and he immediately started talking about how he uses expected value all the time at work. That made me smile, because students always ask about math "when am I going to use this?" It is nice to hear that someone really does!