12.1: Life is Uncertain

Almost everything in life is uncertain, so we can’t help but deal with probabilities. We don’t have any choice. Still, some outcomes are much more likely than others. It is reasonably probable that there will be at least a little snow in Norman, Oklahoma, sometime this year, less probable that there will be over six inches of snow this January, and very improbable that there will be any snow at all in June. In this module, we will study the notion of probability.

Many of the examples in this module involve games of chance. We employ such examples because they are relatively simple, and many of you are familiar with them already. But probability is important in many other settings, and once we learn how it works in these simpler cases, we will see that it turns up almost everywhere. Here are a few of the many cases where we must make important decisions based on uncertain information.

Visiting the Doctor: Often, a person’s symptoms and test results are compatible with several different diagnoses, but some of the diagnoses may be more probable than others. Furthermore, the outcomes of many medical treatments are uncertain. You or a loved one may one day be forced to consider the probability that a risky treatment will improve a very bad medical condition.

Example: suppose that you must weigh the odds of a type of operation in which 65% survive with a much higher quality of life— but 5% of the patients die in surgery.

Selecting a Major: A college degree will make it easier for you to get a job, but it requires a lot of time and money, and it won’t guarantee a good job once you graduate. And once you do decide to attend college, you must select a major. Perhaps the fields you like best offer fewer job opportunities than fields you like less. How should you decide what to major in?

Divorce: There is a reasonable chance that if you get married you will end up getting divorced. According to the US Census Bureau, Florida has the seventh highest divorce rate in the nation. 41% of first marriages end in divorce (along with 60% of second marriages and 73% of third marriages). Of course, few people think that they will be among the casualties, but many of them will be.

Staying Healthy: Smoking cigarettes is risky, but it does offer several short-term benefits. They help you stay calm and relaxed in moments of stress, they keep you alert, and they help prevent overeating. Moreover, there is always someone’s Aunt Edna who smoked four packs a day and lived to be 95. Besides, it is hard to kick the habit (over 70% of people who quit are back on cigarettes within three months). Are they so dangerous that it’s worth trying to quit?

• Similar long-run risks: overeating or excessive drinking pose a risk over the long run. But a little alcohol each day is relaxing and may be good for your health.
• Similar short-term risks: drinking too much before driving or having sex without a condom pose a risk even in the short run.

Raising your Children: There are many gambles here. How strict should you be? What risks should you let them take? How much should you allow them to make their own decisions?

Insurance: When you buy insurance for your car, your home, or yourself, the insurance company is betting that you will not need it. You are hedging your bets by buying it. (This is one bet you hope to lose).

Starting a Business: You would like the independence of owning your own business. Moreover, some small businesses do very well and you could make a lot of money. But many new businesses fail. Is it worth the risk? How can you even determine what the risk is?

Drilling for Oil: Drilling a new well is a risky proposition. It is expensive, and many wells never produce. But some locations are much more likely to yield oil than others. The relevant facts in determining such probabilities include the geological makeup of a region and the number of successful wells in the area.

The Used Car Dealer: You show up on the lot and want to buy a used pickup truck. It looks o.k., you hear that it only has 60,000 miles on it, and the price is right. But there isn’t any long-term warranty.

Seat Belts: Seat belts save many lives. But some people die because they wore a seat belt. Moreover, if you don’t like to be bothered putting them on, they involve costs in time and irritation. And even if you wear seatbelts, you run some risk every time you go somewhere in your car. There are many examples of this sort – wearing a helmet when you ride a bike or a motorcycle, driving way above the speed limit.

Investments: If you begin saving money soon after you graduate, you will have fewer worries about putting your children through college and you will provide for your retirement years. But as the collapse of Enron reminds us, the investments that promise the most gains are typically the riskiest. What should you do?

The Stock Market: No one is sure what the market will do. If it does well, you can make much more money than you could with most other investments. But if the market takes a big dip, like it did in October of 1997 or April of 2000, you can also lose your shirt.

In short, we all must make important decisions that involve uncertainty. For college students, these include questions about what to major in, which courses to take, whether to go to graduate school, whether to study for an exam or hit the bars, whether to end a relationship, and so on.