# How to Find a Probability

## Finding a Probability

A probability is a measure of how likely (how probable) an event is to happen.

Imagine you tossed a coin. What is the probability of the coin landing Heads up?

## How to Find a Probability

### Question

What is the probability of getting Heads in a coin toss?

# 1

Find the number of ways getting Heads can happen.

There is only 1 way of getting Heads.

# 2

Find the total number of outcomes.

There are 2 outomes: getting Heads and getting Tails.

# 3

Divide the number of ways of getting Heads (1) (found in Step 1) by the total number of outcomes (2) (found in Step 2).

Probability of getting heads = 1 ÷ 2 = 0.5

The probability of getting Heads is 0.5.

Using notation, if H is the event of a Heads coming up, the probability of the event is P(H).

We can also express this as a fraction (½) or a percentage (50%).

## A Formula to Find a Probability

The formula for finding a probability is shown below:

$$Probability = \frac{Number~of~ways~an~event~can~happen}{Total~number~of~outcomes}$$

Let's use the formula in an example.

### Question

What is the probability of rolling a 6 on a die?

# 1

$$Probability = \frac{Number~of~ways~an~event~can~happen}{Total~number~of~outcomes}$$

# 2

Find the number of ways the event can happen.

Find the number of ways getting a 1 can happen.

There is only 1 way of rolling a 1.

# 3

Find the total number of outcomes.

There are 6 outomes: getting 1, 2, 3, 4, 5 and 6.

# 4

Substitute the number of ways the event can happen and the total number of outcomes into the formula.

$$Probability = \frac{1}{6}$$

The probability of rolling a 1 is 16.

Using notation, if 1 is the event of rolling a 1, the probability of the event is P(1).

We can also express this as a number (0.167) or a percentage (16.7%).

## Slider

The slider below another real example of how to find a probability.

Open the slider in a new tab