Functional Skills: Probability Tables

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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 1313?

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

Total number of girls =750−396=354= 750 – 396 = textcolor{red}{354}

Total number of students aged 1313 or over =750−287=463= 750 – 287 = textcolor{red}{463}

Total number of girls aged under 1313 =354−225=129= 354 – 225 = textcolor{red}{129}

Total number of boys aged 1313 or over =463−225=238= 463 – 225 = textcolor{red}{238}

Total number of boys aged under 1313 =287−129=158= 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 396396, of which 158158 are aged under 1313

So, the probability is

158396dfrac{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 11 to 55, are spun and the outcomes are added together.

What is the probability that the result is 77?

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 22 on spinner one and 44 on spinner two, then the result is

2+4=62 + 4 = 6

Step 3: Calculate the probability. There are 25textcolor{limegreen}{25} possible outcomes, and 4textcolor{red}{4} of these are 77 (circled in red).

So, the probability is

425=0.16dfrac{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 44 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]

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a) In total, there are

12+14+15+9=5012 + 14 + 15 + 9 = 50 pupils

1414 boys chose to have a packed lunch.

So, the probability is

1450=0.28dfrac{14}{50} = 0.28

 

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

12+15=2712 + 15 = 27

1515 of these are girls.

So, the probability is

1527dfrac{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]

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

196−156=40196 – 156 = 40 unemployed males

254−156=98254 – 156 = 98 employed females

40+32=7240 + 32 = 72 unemployed people in total

98+32=13098 + 32 = 130 females in total

254+72=326254 + 72 = 326 people in total

 

The completed table will look like this:

 

b) There are 326326 people in total. 7272 of these people are unemployed.

So, the probability is

72326=0.221dfrac{72}{326} = 0.221 (33 dp)

Question 3: Two dice, both numbered 11 to 66, 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 1212?

c) What is the probability that the result is over 2020?

[4 marks]

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

The table completed table will look like this:

 

b) There are 3636 results in total.

The result is 1212 a total of 44 times.

Therefore, the probability is

436=19dfrac{4}{36} = dfrac{1}{9}

 

c) The results that are over 2020 are 24, 25, 3024, , 25, , 30 and 3636

The result is over 2020 a total of 66 times out of 3636

Therefore, the probability is

636=16dfrac{6}{36} = dfrac{1}{6}

Additional Resources

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Exam Tips Cheat Sheet

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Formula Booklet

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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

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Probability Tables L2

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