Using probability in real life
This is the most important section of the post, actually. You can use your knowledge of probability to make decisions in real life that are better than the decisions of most people.
You work at a job making $50,000 a year. You decide to take a job making $200,000 a year, even though you estimate that there’s a 25% chance of the company paying you $200,000 a year going bankrupt after your first year of employment.
The expected value of that decision is simple enough.
But let’s look at a more day-to-day practical application. Suppose you’re considering parking in a handicapped spot.
The probability of getting a ticket for this might be 20%, and the parking ticket might be $200. That’s an expected loss of $40.
But parking in that spot will save you half an hour of walking, and you’re a highly paid consultant earning $250 per hour. That means your time is worth $125 per half hour.
Since your time is worth well over $40, it makes financial sense to take the risk.
Of course, that example ignores any moral implications involved. You might have a moral problem with taking up a parking spot intended for a handicapped person.
Here’s another practical example:
You’re obese, and you’re 45 years old. According to the doctor, your life expectancy if you don’t lose weight is 60 years old. But if you have weight loss surgery, your life expectancy becomes 68 years old.
But you also have a 1 in 800 chance of dying during the weight loss surgery.
Let’s assume that the life expectancy numbers are absolute certainties, because that makes the math easier to do.
You have a 100% chance of dying 15 years earlier if you don’t use the surgery. That’s -15 years.
You have a 799/800 chance of gaining 18 years if you have the surgery. That’s an expected gain of +17.98 years.
You also have a 1/800 chance of dying 30 years earlier (at age 45). That’s another -0.04 years in expected loss.
17.98 – 15 – 0.04 = 2.94 years of expected additional life.
And chances are, you’ll enjoy life more during that time. You’ll be able to engage in more activities, find more people to date, and require less medical attention.
You can make the math even more complicated by factoring in the possibility that you could lose the weight without surgery. But we don’t need to get into that much detail; we just wanted to look at how this type of thinking (probability based) can be applied to real life issues to make better decisions.)
You can find an almost unlimited number of gambling probability examples to discuss. But all of them start with the notion that probability is always a number between 0 and 1. The other thing to remember in probability problems is the difference between “or” and “and”. If you want to know the probability of this happening OR that happening, you add the probabilities of each together. If you want to know the probability of this happening AND that happening, you multiply the probabilities by each other.
You can multiply the probability of winning by the amount you win and compare it with the probability of losing and the amount you’ll lose to get the expected value of any bet. In casino games, the edge is always with the house, although the way they present the games is subtle.
It’s not always clearly obvious how the casino gets it mathematical edge over the player. But it’s always there, unless you’re a card counter or expert video poker player.