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Taking a Chance: How Probability Affects Us Every Day

Updated on April 28, 2018

Probability

Probability. Out of all the math that I've learned over my academic career, it has not being trigonometry, calculus, nor algebra that has left as big a legacy as probability. It is one of those revelations that helps change the way you view choices in life. “What's the chance that it rains tomorrow?” affects the type of plans that you decide to make. “What are the odds that that person would like me back?” affects the people that you choose to interact with. “If I try to do that, how likely am I to fail?” affects the challenges that you will take on.

Probability is embedded within our decision-making processes. It influences our actions ranging from things that will change our life to the smaller interactions that we have every day. There’s a famous saying that you miss 100% of the shots that you don't take. That's absolutely true--and probability, on the other hand, helps us determine what type of results to expect from the shots that we do take. The short example below shows how using probability can give us an expected value of, for example, applying to a university.

Tree Diagram of Choice

You have two choices to make: You either do not apply and miss that shot, 100%, and get no value or you apply--you give it your best shot and you take a chance. You know that this particular university only admits 5% of its applicants. Your probability of getting accepted is 5%. That means, there is a 95% chance that you won't be selected. You have your probabilities, so how do you inform your decision? That comes down to the value that you associate with each outcome.

If you don't get accepted, what does it cost you? It costs you your application fee; it costs you the time that you put in; there’s the opportunity cost of what you could've done with all those resources; and there's a feeling of rejection. The value in the circumstance is measured by utility—a measure of your happiness that states in numbers how happy you are with the results. Because being rejected will make you unhappy, let's say you have a -500 value that you assigned to being rejected. On the other hand, because this university is so competitive, there's a likelihood that you may receive a scholarship. The value of this prestigious education combined with the potential scholarship funds gives you a tremendous utility. Let’s assume that this value is 20,000. Given these numbers, you are now able to calculate the expected value of applying to university, and we do this in the following way:

Expected Value of Applying = 20,000 * 0.05 + (-500) * 0.95 = 525.

You can see that by applying, even with a 5% chance of being admitted, the value that you get is higher than by doing nothing and by not applying—a utility of 525 is much higher than a utility of 0. So what do you do?

Probability informs us in this way and it guides us on how we decide to live life. It helps us decide which choices are the right ones and which choices bring justice to ourselves and justice to others. So the next time you face a decision, ask yourself: what's the expected value of doing versus not doing. You'll probably get the right answer.

There Are Also Times When Math Isn't So Much Fun

Photo Credit: graemea00 Gambling Man Blues via photopin (license)

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