Functional Skills: Probability Tables
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.
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 ?


Step 1: Use addition and subtraction to find the missing values in the table, e.g.
Total number of girls
Total number of students aged or over
Total number of girls aged under
Total number of boys aged or over
Total number of boys aged under
Note: This could have been done in a different order with different sums.
Step 2: Find the probability. The total number of boys is , of which are aged under
So, the probability is
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 to , are spun and the outcomes are added together.
What is the probability that the result is ?


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 on spinner one and on spinner two, then the result is
Step 3: Calculate the probability. There are possible outcomes, and of these are (circled in red).
So, the probability is
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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 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
pupils
boys chose to have a packed lunch.
So, the probability is
b) The number of pupils that chose a hot dinner is
of these are girls.
So, the probability is
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.
unemployed males
employed females
unemployed people in total
females in total
people in total
The completed table will look like this:
b) There are people in total. of these people are unemployed.
So, the probability is
( dp)
Question 3: Two dice, both numbered to , 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 ?
c) What is the probability that the result is over ?
[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 results in total.
The result is a total of times.
Therefore, the probability is
c) The results that are over are and
The result is over a total of times out of
Therefore, the probability is
Specification Points Covered
L2.26 – Work out the probability of combined events including the use of diagrams and tables, including two-way tables
L2.27 – Express probabilities as fractions, decimals and percentages
Functional Skills: Probability Tables Worksheet and Example Questions
Probability Tables L2
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