Probability

What is probability?

The definition of probability is simply the likelihood that an event will happen. Probability isn’t a guarantee, but rather a guide of what may occur and how likely it is to occur based on the number of possible outcomes.

Probability is measured from 0 (impossibility) to 1 (certainty) and can be shown as a fraction (⅙), decimal (0.6), or percentage (60%).

(Note: although it exceeds the depth of this article, there are four different types of probability - classical, empirical, subjective, and axiomatic. Learn more about the types of probability here.)

Probability examples

The most straightforward example of probability is a coin toss. Since there are only two possible outcomes - heads or tails - each one has a 50% probability of occuring. Another probability example is rolling a die. There’s a one in six (or 16%) chance that you will roll a four.

Probability formula

Before calculating probability, it’s helpful to understand the specific meaning of a few words in the context of probability.

  • Experiment or trial: this refers to any action where the outcome is uncertain (e.g. rolling dice, spinning a spinner, flipping a coin, etc.).
  • Sample space: this includes all possible outcomes of an experiment (e.g. 36 possible outcomes from rolling 2 dice).
  • Event: this is one or more outcomes from an experiment (e.g. rolling doubles).

Side note: There are a couple different types of events which can impact how the probability is calculated.

  • Independent - Each event is not affected by any other events (e.g. when flipping a coin, each toss is perfectly isolated).
  • Dependent - Each event can be affected by previous events (e.g. drawing names for a gift exchange - once a name is drawn, the remaining possible names to draw from is reduced).
  • Mutually exclusive - Both events can’t happen at the same time (e.g. turning left or right, flipping a coin, etc.).

The basic formula to calculate the probability of an event is to divide the number of ways the event could happen by the total number of possible outcomes.

# of ways the event can happen / # of total possible outcomes = Probability that an event will occur

Using the example of rolling 2 dice, this is how to calculate the likelihood of rolling doubles.

6 (doubles can be rolled 6 different ways) / 36 (total possible outcomes from rolling 2 dice) = 16% (also shown as 0.16 or ⅙) probability of rolling doubles

Obviously, probability gets more complicated when calculating the likelihood of conditional or dependent events such as drawing a red spade followed by a black heart. To learn more about calculating the probability of dependent events, see here.

Probability and the gambler’s fallacy

Sometimes when we’re looking at the probability of future events, past outcomes can play tricks on us. This ‘trick’ is called gambler’s fallacy.

This is also known as the Monte Carlo Fallacy because of an infamous example that occurred at a roulette table there in 1913. The ball fell in black 26 times in a row and gamblers lost millions betting against black, assuming the streak had to end. However, the chance of black is always the same as red regardless of what’s happened in the past, because the underlying probability is unchanged since a roulette table doesn’t have a memory.

Another similar example is assuming a coin that’s landed on heads the past 15 times will land on tails next. However, each toss is independent and the probability remains consistent: 50% for heads and 50% for tails.

Additional resources for learning more about probability