15+ Real Life Examples of Probability

Have you ever wondered about the likelihood of certain events occurring? Or think about the chances that something good or bad will happen? Well, sometimes it may just be probability at play.

But how exactly does probability works in the real world?

According to experts, here are practical and real-life examples of probability in action.

Buying a one-way or round-trip airfare ticket

How can one-way airfare be more expensive than round-trip?

Have you ever tried to buy a one-way ticket, only to discover that you would save money purchasing a round-trip and not flying home? How does that work for the airline company? The answer to this puzzle turns out to be an excellent example of probability calculations.

Right now, if I try to book a one-way ticket from my local airport to Newark sometime in the next two weeks, the non-stop fare is $216. But if I book the same outbound flight as a round trip ticket, my fare drops to $164. That’s a savings of $52! So why would I pay over 30% more to get a one-way ticket?

The answer to this puzzle is that the airline company counts on some customers needing to change their return flight to a different time or date. In doing so, these customers will end up paying any price difference.

For the customer, the extra fare will be less than buying a whole new ticket, but for the airline company, it will make up for the fact that the round-trip was $52 cheaper.

If that alone were the reason for airline companies to sell round-trips at a lower cost than one-ways, you could do a little calculation to see the expected probability that a customer will need to swap out their return ticket for a new time or date.

Let’s say that a new return ticket will cost a customer an extra $208 if they want to make a late-in-the-process change. That extra cash is four times more than the $52 in savings that the airline provided when the customer bought a round-trip instead of a one-way.

This means that the airline is counting on at least one out of four customers needing to make this change.

Does it seem reasonable that 25% of the time, customers make this type of last-minute change to their return ticket? It may seem like a high percentage, but keep in mind that these are the customers that were only planning to book a one-way ticket and just gave their best guess as to when they would come home.

If they are like most people, they might not think to change their return flight to a better time or day until the fares have increased by a lot.

In the end, airlines have many reasons to offer round-trips at a lower cost than one-way tickets. With probability calculations, you can get an idea of some of the trade-offs that might be for these companies and you as a customer.

Rolling a six-sided dice

Probability is the likelihood that a given event will happen, expressed in numeric terms. Rolling dice is an excellent way to understand this idea. A normal six-sided die has a one-in-six chance of rolling a one any time you roll it. 

We could also say that it has about a 17% chance of rolling a one. What happens if we want to determine the probability of something more complicated?

Repeated rolls

If the odds of rolling a one on a six-sided die are one in six, then what are the odds of doing that twice in a row? Or three times? To figure this out, we multiply our probabilities. 

If our odds of a one are one in six, then our odds of two ones in a row are one in 36. We multiply the fraction 1/6 by itself, meaning that we multiply the numerators and the denominators separately. 1×1 = 1. 6×6 = 36.

For three dice, we multiply by 1/6 one more time to get one in 216.

Results are independent

The odds of rolling a one on a six-sided die are one in six. This is true no matter how many times we roll that dice or how many times we have already rolled a one. 

If we’re trying to roll three ones in a row, and we’ve just moved two ones, the odds that the next die comes up as a one are exactly one in six, not one in 216. This is because each die roll is calculated separately.

In other words, the past rolls of the dice will not have any direct impact on the next roll we make. 

Research and forecasting on post-pandemic disability and employment

Stephen Haller, General Counsel for the IRS, and I conducted research and forecasting on post-pandemic disability and employment starting in August of last year. It culminated in several scholarly articles.

More specific data: My goal was to forecast the percentage of people newly disabled by COVID in the State of Iowa. The first equation I constructed used historical information on the disabling rate of each major conflict since Iowa achieved statehood. 

The second was the infection rate of COVID, keeping in mind rates are variance equations themselves. Next, I incorporated the mortality rate of the disease. Lastly, I added qualitative information from the Mayo Clinic to define COVID’s disabling rate. 

My forecast is likely wrong by about 2.45%, and I invite you to understand my error in the spirit of collaboration. I had determined that COVID yielded a disabling rate of 19.21% per infection as a function of the mortality rate. 

A later study conducted by Oxford University showed those who survived infection from Coronavirus in the United Kingdom yielded a net disabling rate of 37%. 

My forecast was about Iowa’s disabling rate based on the Mayo Clinics definitions. Oxford’s forecast was more of an analysis of raw data transforming it into information using different definitions for “disabled.” 

My forecast predicted the infection rate per infection in each person. Later in the pandemic, we learned that the unvaccinated were becoming reinfected at a rate between nine and 13 months. That means most of Iowa and the UK population were infected twice before the majority vaccination. 

When 19.21% is squared (representing the two infections), my forecast yields a 34.73% disabling rate. That is the marvel of multiple forecasting—its simplistic precision appears almost dynamic compared to conventional taxational forecasting models. 

Thus, I pose this question to the reader writ-large, why does taxation, a qualitative science within the law, not use multiple model forecasting?  

The odds of winning the lottery if you buy one ticket each week

I have played the lottery off and on for years, and the lotto is a great way to conceptualize probability. 

I am going to use my state’s rules for an example:

On average, most states have around 10 million people playing the lottery each week. In terms of the probability, that would mean that there are 100 million possible outcomes each week on average.

Out of those 100 million possible outcomes, there are six numbers chosen, so the odds of getting your six consecutive numbers correct if you choose to play just one ticket = 1/6 (16.667%).

The probability that someone wins when they play just one ticket = 1/100,000,000 (0.000001).

The odds of winning the lottery if you play one ticket each week = 1/100,000,000 (0.000001) ≈ 0.00000001 or 0.00000001%.

A child getting a cookie

We use probability anytime there is uncertainty. It helps us make decisions. Get what we want. For example, a child wants a cookie. Their mom just gave them a cookie. They ate it, and it was delicious, so now they want another.

The child will quickly calculate which scenario will give them the highest probability of a cookie. And they will ask the other parent when the mom is out of earshot because that will give them the highest probability of receiving a cookie.

Safety and risk factors on building and construction sites

On the building and construction site, safety is essential. The unexpected can always happen. However, there has to be a balance between working and being safe. 

Site safety comes down to predicting the probability of risks and defining the risk factor for each situation. So we can focus the most extensive efforts where there is a higher probability of an accident and a higher level of risk.

1. First, we define the level of risk if an accident occurs as either a minor injury, serious injury, long-term injury, or death. 
2. Then we determine if a risk can be eliminated, isolated, or only minimized by using safer building methods, better PPE (personal protective equipment), technology, safer tools, better training, or hiring specialized workers. 

By doing all these, we can make the building site safer and reduce the chance and probability of a severe accident.

Recovering from debts

I work in business-to-business debt collection, and our clients are keenly interested in the probabilities of recovering their debts. We closely monitor the probabilities inherent in our work.

For example, the probability we collect on outstanding debt is 85%, and we are able to negotiate a settlement without needing to bring the debtor to court 97% of the time. By sharing these probabilities with our clients, they can make a more informed decision about our services.

Knowledge of probabilities ensures that decisions can be objective and data-driven instead of based on instinct.

Buying cryptocurrencies

If you’ve ever thought of buying crypto, chances are you know that the most probable outcome for every new coin is — failure. 

Nobody knows the exact number of dead coins (maybe because anyone can make a new coin and watch it die a quick death), but one thing is sure: several thousand cryptocurrencies have been around at one point or another, only a handful of them have survived to tell the story.

But how to calculate the probability that a new coin will survive? It’s simple — don’t even try; because the probability of such an outcome is ridiculously high, the exact percentage doesn’t even matter. 

So if you want to buy crypto, this probability of failure should teach you a lesson that unless you’re a daredevil, you should only invest in well-established coins and only as much as you’re ready to lose. It’s because the probability of failure is not the only one. 

There’s also the probability that its price will plummet at a certain point, and it’s also relatively high. The only thing mitigating it is the probability (even higher) that it will rise again, as it always has!

Insurance and the worst-case scenarios

Insurance is a great real-life example of probability. We pay to secure ourselves or assets from the probability of accidents, loss, theft, or damage, but in reality, we are not 100% certain that any of this will ever happen.

In this case, the negative effects of something bad happening to our assets or ourselves are far too big to leave it to chance, so we feel safer paying for the insurance.

It’s tough to predict if the worst-case scenario will actually happen to us. Though car and home insurance is a fee we are obligated to pay, we also pay insurance voluntarily in many cases.

Take travel insurance as an example. It gives us peace of mind to know that if our flights are canceled or our luggage is lost, we will be fully covered and our money refunded.

Even if our trip goes according to plan, when the negative effect of not paying insurance is far too significant, we find a way to be ok with paying for what, in reality, is just a probability.

Everything is a possibility

Probability is essentially research into a series of events that may or may not occur. In everyday life, everything is a possibility, from weather predictions to the chance of dying in an accident. We don’t even realize we’re doing it most of the time. 

For instance, before heading out for personal or professional reasons, we look at the weather forecast. Meteorologists can’t predict the weather accurately; therefore, they rely on tools and instruments to anticipate rain, snow, or hail. 

Meteorologists also use historical data to forecast high and low temperatures and possible weather patterns for the day or week ahead.

Meeting someone taller than me

What are the odds that I meet someone taller than me today? 

I am 5’7″ tall, so the probability that someone I meet today will be taller than me = 1/2 (50%).

I live in a city of roughly 200,000 people. The probability that I meet someone at all today = ~1/200,000 (0.00005). The probability of meeting someone who is taller than me today = 1/2 (50%) X 1/200,000 (0.00005) ≈ 0.00000025 or 0.00000025%.

Tossing a coin in cricket game

Before starting any cricket match, a toss is done by the referee between the opposing teams. The toss-winning squad got the chance of choosing batting or bowling. They can choose batting or bowling as per their desire.

Although coins only have two faces, head or tail, and both have 1 out of 2 chances of coming, there is a 50% probability of both teams winning the toss.

Winning the lottery

Lottery tickets are one of the most remarkable examples of probability. Suppose we have to choose a number which is the same six-digit number, written on the winning ticket. So, there exists only one chance out of 1 lakh of getting the same number.

Predicting the weather

Probability is the most binding domain of weather forecasting. Based on previous analysis, meteorologists predict future conditions like 70% rain in any area, 10cm rain in any area, or many more. However, the whole weather forecast is 40% depending on probability.

These predictions are sometimes very accurate and sometimes are entirely contradictory. Meteorologists also predict the danger of natural disasters; only the difference is that different domains are considered in weather forecasting and natural disaster prediction.

Getting heads on a coin toss

One of the easiest examples of probability is a simple coin toss where you have a coin with only two sides, one of which is heads. If you flip the coin, then there are two main ways this can play out — it comes up tail, or it comes up heads. 

When we talk about the probability of getting heads on a single coin toss, what exactly are we saying? We are asking how likely we think it is that we get heads when we flip a coin.

Since we know the only possible outcomes of a single coin toss are either heads or tails, each result must carry some probability. In other words, the probability of getting heads on a single coin toss = 1/2 (50%)

Spotting and solving problems in eCommerce marketing

I work in eCommerce marketing, and I love to collect data about our business and use it to calculate probabilities that can help us improve our marketing strategies. 

For example, our data shows us that there is a probability of 53.47% that a customer will abandon a shopping cart before checkout. To address this, we have an email campaign that automatically follows up on abandoned carts. 

The probability of these follow-up emails being opened is 47.03%, much higher than the 21% probability an average email is opened.

Therefore, by calculating probabilities, we can spot a problem and identify the best way of resolving it.

Having an insurance plan

Probability aids in determining the appropriate insurance plan for you and your family. For example, if you are a heavy smoker, your chances of developing lung illness are higher.

So, instead of choosing an insurance plan for your car or home, you should consider health insurance first because the chances of becoming ill are higher.

People nowadays, for example, get insurance for their mobile phones since they are aware that the odds of their phones being destroyed or lost are considerable, I believe.

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