New
New
Year 9

Problem solving with theoretical probability

I can use my knowledge of probability to solve problems.

New
New
Year 9

Problem solving with theoretical probability

I can use my knowledge of probability to solve problems.

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Lesson details

Key learning points

  1. Knowledge of probability can be applied to real world situations .
  2. Probabilities can be used to aid decision making.
  3. 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.

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.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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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?
An image in a quiz
5
6
Correct answer: 7
8
9
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 $${3}\over{36}$$?
An image in a quiz
2
Correct answer: 4
6
8
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?
An image in a quiz
$${1}\over{6}$$
$${5}\over{6}$$
$${4}\over{15}$$
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

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?
An image in a quiz
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?
An image in a quiz
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?
An image in a quiz
$${1}\over{8}$$
$${5}\over{8}$$
$${4}\over{12}$$
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?
An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
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?
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
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
An image in a quiz
An image in a quiz
An image in a quiz