Basic Probability in Science

Probability measures how likely something is to happen, on a scale from \(0\) (impossible) to \(1\) (certain). Science uses it constantly — in genetics, in predicting weather, in judging whether a result could have happened by chance. The core idea is simple enough to learn in a few minutes, and it turns up in more test questions than you might expect.

This lesson shows you the basic probability formula and how to use it on everyday examples.

The Basic Formula

For equally likely outcomes, probability is a fraction: \[ P(\text{event}) = \dfrac{\text{number of favorable outcomes}}{\text{total number of outcomes}}. \] Rolling a \(3\) on a six-sided die has one favorable outcome out of six total, so \[ P(3) = \dfrac{1}{6}. \] Drawing a red card from a standard deck has \(26\) favorable outcomes out of \(52\), so \[ P(\text{red}) = \dfrac{26}{52} = \dfrac{1}{2}. \] You can leave answers as fractions, decimals, or percents; \(\dfrac{1}{2}\) is the same as \(0.5\) or \(50\%\).

Reading the Scale

Because probability runs from \(0\) to \(1\), the size of the number tells you the likelihood. A probability near \(0\) means unlikely; near \(1\) means very likely; exactly \(\dfrac{1}{2}\) means an even chance. If a question offers an answer greater than \(1\) or less than \(0\), it must be wrong — probabilities cannot leave that range.

The Complement: The Chance It Does NOT Happen

Sometimes it is easier to find the chance an event does not happen. Because all outcomes together have probability \(1\), \[ P(\text{not event}) = 1 – P(\text{event}). \] If the chance of rain is \(0.3\), the chance of no rain is \(1-0.3 = 0.7\). This shortcut saves time when the “not” outcome is simpler to count.

Watch: A Short Video Lesson

mathantics walks through this skill clearly in a few minutes. It is a helpful companion to the reading above:

A Routine for Probability Questions

1. Count the favorable outcomes and the total outcomes.
2. Write the probability as \(\dfrac{\text{favorable}}{\text{total}}\).
3. Simplify, and convert to a decimal or percent if needed.
4. For “not” questions, subtract from \(1\).

Practice

1. What is the probability of rolling an even number on a six-sided die?
2. A bag has \(4\) red and \(6\) blue marbles. What is \(P(\text{red})\)?
3. From the same bag of 4 red and 6 blue marbles, what is \(P(\text{not red})\)?
4. If \(P(\text{event}) = 0.8\), what is \(P(\text{not event})\)?
5. Can a probability be \(1.4\)? Why or why not?
6. What does a probability of \(0\) mean?

Answers

1. \(\dfrac{3}{6} = \dfrac{1}{2}\).
2. \(\dfrac{4}{10} = \dfrac{2}{5}\).
3. \(1 – \dfrac{2}{5} = \dfrac{3}{5}\).
4. \(1 – 0.8 = 0.2\).
5. No — probabilities must be between \(0\) and \(1\).
6. The event is impossible.

Where This Fits in Your Science Prep

Basic probability leads into counting outcomes and compound probability, and it supports reasoning about whether results happened by chance. It also appears in genetics through Punnett squares. See all topics on the Science Topics Hub.