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# Finding a Probability

(KS3, Year 7)

## 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

There is only

**Heads**can happen.There is only

**1**way of getting**Heads**.# 2

Find the total number of outcomes.

There are

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

There is only

*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

There are

*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%).

## A Note on Notation

The probability of an event can be written as:*P(Event)*

**H**be the event that a coin lands on

**H**eads when it has been tossed. We can denote the probability of getting heads as:

*P(H)*

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