The Lesson

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?

Step-by-Step:

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

Answer:

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?

Step-by-Step:

1

Start with the formula.
$$Probability = \frac{Number~of~ways~an~event~can~happen}{Total~number~of~outcomes}$$

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

Answer:

The probability of rolling a 1 is 1⁄6. 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%).

Lesson Slides

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

A Note on Notation

The probability of an event can be written as:
P(Event)
A letter or symbol can be used to represent an event. For example, let H be the event that a coin lands on Heads when it has been tossed. We can denote the probability of getting heads as:
P(H)