# Functional Skills: Probability Tables

## Functional Skills: Probability Tables Revision

**Probability Tables**

You may need to use **tables** or **diagrams** to help you find probabilities.

There are **2** types of probability table that you will need to understand.

Make sure you are happy with the following topics before continuing.

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**Type 1: Two-Way Tables**

One type of table you will encounter is a **two-way table**.

**Example:** The table shows some information about the ages of boys and girls in a school.

A boy is chosen at random. What is the probability that the boy is aged under 13?

**Step 1:** Use addition and subtraction to find the missing values in the table, e.g.

Total number of girls = 750 - 396 = \textcolor{red}{354}

Total number of students aged 13 or over = 750 - 287 = \textcolor{red}{463}

Total number of girls aged under 13 = 354 - 225 = \textcolor{red}{129}

Total number of boys aged 13 or over = 463 - 225 = \textcolor{red}{238}

Total number of boys aged under 13 = 287 - 129 = \textcolor{red}{158}

**Note:** This could have been done in a different order with different sums.

**Step 2:** Find the probability. The total number of boys is 396, of which 158 are aged under 13

So, the probability is

\dfrac{158}{396}

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**Type 2: Tables for Multiple Events**

When there are two events, it is useful to write down all possible results in a **table for multiple events**. You can then find probabilities using the table.

**Example:** Two spinners, both numbered 1 to 5, are spun and the outcomes are added together.

What is the probability that the result is 7?

**Step 1:** Draw a table to write down all possible results, as shown.

**Step 2:** Fill in the table with the results, e.g. if you land on 2 on spinner one and 4 on spinner two, then the result is

2 + 4 = 6

**Step 3:** Calculate the probability. There are \textcolor{limegreen}{25} possible outcomes, and \textcolor{red}{4} of these are 7 (circled in red).

So, the probability is

\dfrac{\textcolor{red}{4}}{\textcolor{limegreen}{25}} = 0.16

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## Functional Skills: Probability Tables Example Questions

**Question 1:** Pupils in a school can either choose to have a hot dinner or packed lunch. The table below shows some information about the choices of the Year 4 pupils.

**a)** One of the pupils is chosen at random. What is the probability that they have a packed lunch and are a boy? Give your answer as a decimal.

**b)** One of the pupils that chose a hot dinner is chosen at random. What is the probability that they are a girl?

**[3 marks]**

**a)** In total, there are

12 + 14 + 15 + 9 = 50 pupils

14 boys chose to have a packed lunch.

So, the probability is

\dfrac{14}{50} = 0.28

**b)** The number of pupils that chose a hot dinner is

12 + 15 = 27

15 of these are girls.

So, the probability is

\dfrac{15}{27}

**Question 2: **The table below shows some information about the number of employed and unemployed people in a village.

**a)** Complete the two way table.

**b)** Find the probability that a person chosen at random is unemployed. Give your answer to three decimal places.

**[5 marks]**

**a)** Complete the table using addition and subtraction, e.g.

196 - 156 = 40 unemployed males

254 - 156 = 98 employed females

40 + 32 = 72 unemployed people in total

98 + 32 = 130 females in total

254 + 72 = 326 people in total

The completed table will look like this:

**b)** There are 326 people in total. 72 of these people are unemployed.

So, the probability is

\dfrac{72}{326} = 0.221 (3 dp)

**Question 3:** Two dice, both numbered 1 to 6, are rolled together. Their scores are multiplied together.

**a)** Complete the table below to show the possible results.

**b)** What is the probability that the result is 12?

**c)** What is the probability that the result is over 20?

**[4 marks]**

**a)** Multiply each number in each row with each number in each column.

The table completed table will look like this:

**b)** There are 36 results in total.

The result is 12 a total of 4 times.

Therefore, the probability is

\dfrac{4}{36} = \dfrac{1}{9}

**c)** The results that are over 20 are 24, \, 25, \, 30 and 36

The result is over 20 a total of 6 times out of 36

Therefore, the probability is

\dfrac{6}{36} = \dfrac{1}{6}

## Functional Skills: Probability Tables Worksheet and Example Questions

### Probability Tables L2

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