Probability Distribution: Definition, Formula & Example

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  • 0:00 Probability
  • 0:41 Probability Distribution
  • 1:59 Non-Uniform…
  • 2:41 Cumulative Distribution
  • 3:58 Lesson Summary
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Lesson Transcript
Instructor: Lance Cain
Probability distribution is a way of mapping out the likelihood of all the possible results of a statistical event. In this lesson, we'll look at how that is done and how to make practical applications of this concept.


Probability is the likelihood that an event will occur and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. The simplest example is a coin flip. When you flip a coin there are only two possible outcomes, the result is either heads or tails. And so, the probability of getting heads is 1 out of 2, or ½, or 50%. The table below shows the distribution of the probability of each outcome. There is a 50% chance the outcome will be heads, and there is a 50% chance the outcome will be tails.

Probability Distribution Table 1.1
Coin Flip Probability Distribution1

Probability Distribution

Probability distribution maps out the likelihood of multiple outcomes in a table or equation. If we go back to the coin flip example, we already know that one flip of the coin has only two possible outcomes. But if we flip the coin twice in a row, there are four possible outcomes (heads-heads, heads-tails, tails-heads and tails-tails). So now that we have a series of potential outcomes, consider the probabilities of getting heads once, twice or zero times.

Probability Distribution Table 1.2
Coin Flip Probability Distribution2

The table below shows the distribution of probabilities for each possible result of getting heads in two flips of the coin, thus the table is called a probability distribution. Notice that the two middle rows both reflect the probability of getting just one heads in both flips, so these two probabilities can be combined and rewritten as a probability of 2 out of 4, or ½, or 50%.

Probability Distribution Table 1.3
Coin Flip Probability Distribution3

Another plain example is that of rolling a die. A fair die has six-sides, with each side numbered from 1 to 6. Additionally, each side is equally likely to turn up when rolled. A probability distribution can be compiled like the table below, which shows the probability of getting any particular number on one roll:

Probability Distribution Table 1.4
Die Roll Probability Distribution1

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