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Lesson 13 of 13

Year 9

Problem solving with theoretical probability

I can use my knowledge of probability to solve problems.

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Lesson 13 of 13

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Year 9

Problem solving with theoretical probability

I can use my knowledge of probability to solve problems.

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These resources were made for remote use during the pandemic, not classroom teaching.

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Lesson details

Key learning points

Knowledge of probability can be applied to real world situations .
Probabilities can be used to aid decision making.
Theoretical probabilities come from long-term behaviour and therefore may not be seen in the short-term.

Keywords

Sample space - A sample space is all the possible outcomes of a trial. A sample space diagram is a systematic way of producing a sample space.
Tree diagram - Tree diagrams are a representation used to model statistical/probability questions. Branches represent different possible events or outcomes.
Outcome table - An outcome table is a table that shows all the possible outcomes.

Common misconception

When increasing a probability by 50%, pupils may choose to add 50% onto the existing probability rather than multiplying by 1.5.

Make links to any previous work pupils may have done on increasing by a percentage and emphasise that a percentage increase is being applied to the probability.

To help you plan your year 9 maths lesson on: Problem solving with theoretical probability, download all teaching resources for free and adapt to suit your pupils' needs...

Task A could be extended by asking pupils to investigate other possible pairings of dice and writing summaries that advise which pair of dice is optimal for rolling different totals.

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This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Prior knowledge starter quiz

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6 Questions

Q1.
The table shows the possible outcomes when two six-sided dice are rolled and their numbers are summed. Which outcome is most likely to happen?

Correct answer: 7

Q2.
The table shows the possible outcomes when two six-sided dice are rolled and their numbers are summed. Which outcomes have a probability of $${3}\over{36}$$?

Correct answer: 4

Correct answer: 10

Q3.
The table shows the possible outcomes when two six-sided dice are rolled and their numbers are summed. What is the probability that the dice sum to 5?

$${1}\over{6}$$

$${5}\over{6}$$

$${4}\over{15}$$

Correct answer: $${4}\over{36}$$

$${5}\over{36}$$

Q4.
Which calculation would increase 80 by 50%?

$$80 \times 0.5$$

Correct answer: $$80 \times 1.5$$

$$80 \times 50$$

$$80 \times 150$$

Q5.
Increase 20 by 40%.

Correct Answer: 28, twenty eight

Q6.
What is 1.5% of 1000?

Correct Answer: 15, fifteen

Assessment exit quiz

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6 Questions

Q1.
Two dice are rolled and their values are added together. Assuming I drew the table as efficiently as I could, how many sides are on each dice?

Correct answer: 4 and 8

4 and 6

8 and 10

6 and 6

Q2.
The table shows the sample space for when two 8-sided dice are rolled and their values are added together. Which is the most likely outcome?

Correct Answer: 9, nine

Q3.
The table shows the sample space for when a 6-sided dice and a 4-sided dice are rolled and their values are added together. What is the probability that the dice sum to 5?

$${1}\over{8}$$

$${5}\over{8}$$

$${4}\over{12}$$

Correct answer: $${4}\over{24}$$

$${5}\over{24}$$

Q4.
The tables show the sample space for scenarios where two dice are rolled and their values are added together. Which sample space has the greatest probability of the dice summing to 9?

Correct Answer: An image in a quiz

Q5.
The tables show the sample space for scenarios where two dice are rolled and their values are added together. Which sample space has the greatest probability of the dice summing to 7?

Correct Answer: An image in a quiz

Q6.
The tables show the sample space for scenarios where two dice are rolled and their values are added together. Which sample space has the greatest probability of the dice summing to 6?

Correct Answer: An image in a quiz

Problem solving with theoretical probability

Problem solving with theoretical probability

These resources were made for remote use during the pandemic, not classroom teaching.

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

How to plan a lesson using our resources

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.The table shows the possible outcomes when two six-sided dice are rolled and their numbers are summed. Which outcome is most likely to happen?

Q2.The table shows the possible outcomes when two six-sided dice are rolled and their numbers are summed. Which outcomes have a probability of $${3}\over{36}$$?

Q3.The table shows the possible outcomes when two six-sided dice are rolled and their numbers are summed. What is the probability that the dice sum to 5?

Q4.Which calculation would increase 80 by 50%?

Q5.Increase 20 by 40%.

Q6.What is 1.5% of 1000?

Assessment exit quiz

6 Questions

Q1.Two dice are rolled and their values are added together. Assuming I drew the table as efficiently as I could, how many sides are on each dice?

Q2.The table shows the sample space for when two 8-sided dice are rolled and their values are added together. Which is the most likely outcome?

Q3.The table shows the sample space for when a 6-sided dice and a 4-sided dice are rolled and their values are added together. What is the probability that the dice sum to 5?

Q4.The tables show the sample space for scenarios where two dice are rolled and their values are added together. Which sample space has the greatest probability of the dice summing to 9?

Q5.The tables show the sample space for scenarios where two dice are rolled and their values are added together. Which sample space has the greatest probability of the dice summing to 7?

Q6.The tables show the sample space for scenarios where two dice are rolled and their values are added together. Which sample space has the greatest probability of the dice summing to 6?

Q1.
The table shows the possible outcomes when two six-sided dice are rolled and their numbers are summed. Which outcome is most likely to happen?

Q2.
The table shows the possible outcomes when two six-sided dice are rolled and their numbers are summed. Which outcomes have a probability of $${3}\over{36}$$?

Q3.
The table shows the possible outcomes when two six-sided dice are rolled and their numbers are summed. What is the probability that the dice sum to 5?

Q4.
Which calculation would increase 80 by 50%?

Q5.
Increase 20 by 40%.

Q6.
What is 1.5% of 1000?

Q1.
Two dice are rolled and their values are added together. Assuming I drew the table as efficiently as I could, how many sides are on each dice?

Q2.
The table shows the sample space for when two 8-sided dice are rolled and their values are added together. Which is the most likely outcome?

Q3.
The table shows the sample space for when a 6-sided dice and a 4-sided dice are rolled and their values are added together. What is the probability that the dice sum to 5?

Q4.
The tables show the sample space for scenarios where two dice are rolled and their values are added together. Which sample space has the greatest probability of the dice summing to 9?

Q5.
The tables show the sample space for scenarios where two dice are rolled and their values are added together. Which sample space has the greatest probability of the dice summing to 7?

Q6.
The tables show the sample space for scenarios where two dice are rolled and their values are added together. Which sample space has the greatest probability of the dice summing to 6?