How to think about probability? A non-mathematical way

Our life is filled with randomness. Think about it for a minute, how many days in your life have you had, where an entire day went exactly the way you had planned down to the second? I’m gonna safely respond — none. That’s just the nature of the world we live in. We don’t live in a certain world, where things always fall in place as we plan. Rather we live in a world filled with uncertainty or randomness, where essentially we may have some knowledge of what might happen, but are not sure if it will happen.

Uncertainty makes decision-making difficult. And prone to errors. To make better decisions, understanding randomness better is key. And this is where probability comes in.

Probability helps us structure and quantify randomness and assess it more rationally and objectively

Essentially, Probability = Likelihood, of something happening or not. This of course is an over-simplistic definition.

Before going further, let me ask you a question, what do you think is your chance of flipping a coin and getting heads? Even if have never heard anything related to probability, you can easily visualize that flipping a coin could only have two potential possibilities. One is the coin lands heads, and the second it lands tails. So the chance of heads is 1/2 (one out of two potential scenarios) or 50%.

Coin flipping is an overused example, but it is simple to understand the concept. Let’s break this example further to bring out key building blocks of understanding probability.

1. To understand probability, you first need to understand the total number of possible outcomes. In our example, there are only two possible outcomes for a single flip: heads or tails.
2. Probability can never be negative or beyond 100% — this should be intuitive, think about the coin flip once again, can you have a chance of heads -50%? No, why? — Because, at worst the probability of an event not happening (heads not coming) is zero. It can never be negative.

At the same time, the probability can also not exceed 100% — can you have a 105% chance of getting heads? No — At most, the chance can be 100%, and hence, the probability of an event (in our example a coin flip) always varies between 0 and 1 or 0% and 100%

So where can probability be used?

Probability has wide-ranging applications, let me take 3 areas with different examples where probability would be useful:

1. Probability of a particular event happening — Similar to the coin flip example above, we have a host of real-life situations where the outcome is numbered and usually binary in nature. Let’s take a user visiting an e-commerce website, will the user find a product or not? will the user purchase or not? will the user use a particular payment method or not? will the user react more to a new design on the website or not? All these are examples where essentially you are trying to figure out the possibility of an event occurring.
2. Probability of a cluster (group of interest) of events happening — To be precise, here you are asking a different set of questions. For example, what percentage of your clients would be repeat customers? How many new customers are you likely to attract if you run a 10% off or a 20% off? At what rate should you produce so that your team always has a minimum of 10% of their office time available for focusing on improvements?
3. Probability of events when something has already happened — in mathematical terms, this is called conditional probability. But, to understand it we can think of reassessing the chance of something happening(event) as we get more information about some other event that could impact the chance for this event. Let’s take a simple example, say you run a bakery shop and have only the last 2 pieces of bread available for sale. A customer walks in and chooses one of the two pieces of bread. Given this has happened what is the chance that the next customer who walks in will pick up the last remaining bread? You would agree, that the selection of one bread can impact the selection of the last bread remaining.
4. Few example, what are the chances of a person purchasing product B given he/she has already purchased product A? What is the probability of you applying for a role and getting it, given you have relevant experience for the role? Should a company scale up given it has had good revenue growth in the past few quarters?

To conclude, the probability is a way of thinking about random and uncertain events. It helps us give structure to our thought process and quantify the chance associated with our specific interests.

Photo by Caleb Jones on Unsplash