Statistics How To

Random Event: Definition, How to Find Probability

Probability and Statistics > Probability > Probability of a Random Event

What is a Random Event?

A random event is something unpredictable. As it is unpredictable, you can never give it an exact value / probability. For example, you couldn’t predict the probability of you falling down a flight of stairs in the next ten years, as that’s a completely random event. The opposite of random is deterministic, which means it can be calculated exactly. For example, your height can be calculated to the nearest inch, so height is deterministic.

Probability of a Random Event: Overview

probability of a random event

This particular example will guide you through solving random-event problems that give a percentage (e.g. 76% of Americans are in favor of Universal Health Care), then ask you to calculate the probability of picking a certain number (e.g. 3 people) and having them all fall into a particular group (in our case, they are in favor of health care).

For more problem types centered around probability, check out the main probability index.

Probability of a Random Event: Steps

Sample question: 76% of Americans support Obamacare. What is the probability that a randomly selected group of 3 people will all be in favor of Obamacare?

Step 1: Change the given percentage to a decimal. In our example:
76% = 0.76.

Step 2:. Multiply the decimal found in step 1 by itself. Repeat for as many times as you are asked to choose an item. For example, if you were to pick 3 items at random, multiply 0.76 by itself 3 times:

0.76 x 0.76 x 0.76 = .4389 (rounded to 4 decimal places).

That’s how to find the probability of a random event!

Tip: You may be wondering why the probability will continue to go down (0.76 x 0.76 x 0.76 x 0.76 x 0.76 x 0.76 = .19) when the question states 76% of people are in favor. If you think about the odds (76%) than means roughly 1 out of every 4 people you ask will NOT support Obamacare. It would be fairly impossible to ask 8 or more people in a row and have them all support Obamacare.

Check out our YouTube channel for more stats help and tips!


If you prefer an online interactive environment to learn R and statistics, this free R Tutorial by Datacamp is a great way to get started. If you're are somewhat comfortable with R and are interested in going deeper into Statistics, try this Statistics with R track.

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Random Event: Definition, How to Find Probability was last modified: October 15th, 2017 by Stephanie

3 thoughts on “Random Event: Definition, How to Find Probability

  1. Aku

    If a random event is defined as:
    A random event is something unpredictable. As it is unpredictable, you can never give it an exact value or probability.

    Then how you go about calculating a probability for a random event? I mean don’t you guys first say you CANNOT give it an exact value or PROBABILITY, then how do you go about and give it a probability?

    I cannot comphrehend this.

  2. Andale

    From the Google dictionary, a random event is:
    “not able to be predicted.
    “the unpredictable weather of the Scottish islands”
    (of a person) behaving in a way that is not easily predicted.
    “he is emotional and unpredictable””
    So, for example, weather is unpredictable but that doesn’t mean we can’t assign a probability to it. Just not an EXACT one.

  3. Walter G

    A recent survey of top 100 hotels had the following:

    2 hotels on a score of 95.20
    3 hotels on 95.45
    3 hotels on 95.64
    2 hotels on 95.77
    2 hotels on 95.78
    3 hotels on 96.00
    2 hotels on 95.84
    2 hotels on 96.26
    2 hotels on 96.30
    3 hotels on 96.71
    2 hotels on 96.88
    2 hotels on 98.00

    In a reader survey that ranges in theory from 0-100 – what is the probability of so many hotels accumulating the same votes to 4 decimal places ?