New
New
Year 11
Higher

Experimental probability

I can decide if a game/object is fair and calculate the experimental probability.

New
New
Year 11
Higher

Experimental probability

I can decide if a game/object is fair and calculate the experimental probability.

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Lesson details

Key learning points

  1. A set of results can be critically evaluated to help determine if a game/object is fair
  2. Different samples and may affect your perception of fair
  3. The experimental probability of an outcome/event can be calculated from a set of results
  4. Experimental probabilities can be used to estimate an event may occur in a set number of trials

Keywords

  • Experimental probability - The frequency of an outcome from an experiment can be used to produce an experimental probability. This is sometimes referred to as relative frequency.

  • Fair - A trial or experiment is fair if each outcome has an equal chance of happening. Each outcome is said to be equally likely.

  • Bias - If there is bias, in a trial or experiment, the outcomes are not equally likely.

Common misconception

If outcome A occurs more often than outcome B, during an experiment, pupils may conclude that outcome A has a greater probability of occurring than outcome B in future trials.

Even when two outcomes are equally likely to happen, one may occur more often than the other due to chance. You could be more confident about your conclusion if you observe a large difference in results in an experiment with a large number of trials.

Aspects of the lesson can be made practical by replicating some of the experiments in the classroom. The lesson also contains some links to Desmos files which can be used to simulate the experiments virtually.
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.
Two or more events are are mutually __________ if they share no common outcome.
Correct answer: exclusive
exhaustive
inclusive
Q2.
A survey asked people whether they lived in Oakfield or not, and if they last shopped by online delivery or by going in-store. A random person is selected. Match each event to its probability.
An image in a quiz
Correct Answer:P(lives in Oakfield),$$125\over200$$

$$125\over200$$

Correct Answer:P(doesn't live in Oakfield),$$75\over200$$

$$75\over200$$

Correct Answer:P(shops in-store),$$130\over200$$

$$130\over200$$

Correct Answer:P(shops online),$$70\over200$$

$$70\over200$$

Correct Answer:P(lives in Oakfield and shops online),$$45\over200$$

$$45\over200$$

Correct Answer:P(lives in Oakfield and shops in-store),$$80\over200$$

$$80\over200$$

Q3.
A swimming club has 80 members. There are 8 members who swim both front crawl (FC) and butterfly (BF). The value of $$x$$ is .
An image in a quiz
Correct Answer: 10
Q4.
This probability tree shows the probability of one of two events occurring. The value of $$x$$ is .
An image in a quiz
Correct Answer: 0.45
Q5.
Lucas and Izzy each play one game of squash that they can either win or lose. P(Lucas wins) = 0.6, P(Izzy wins) = 0.7. Use the probability tree to find the probability that they both win their game.
An image in a quiz
0.12
0.13
0.18
Correct answer: 0.42
0.7
Q6.
Lucas and Izzy each play one game of squash that they can either win or lose. P(Lucas wins) = 0.6, P(Izzy wins) = 0.7. The probability that at least one of them wins their match is .
An image in a quiz
Correct Answer: 0.88

6 Questions

Q1.
An probability can be determined by the number of times an event occurred during multiple trials.
Correct Answer: experimental
Q2.
Select the biased spinners.
Correct Answer: An image in a quiz
An image in a quiz
An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
Q3.
A toy brick that is dropped could land in one of four possible ways. Sofia drops the toy brick multiple times. Starting with the least likely outcome, place the outcomes in order of likelihood.
An image in a quiz
1 - Outcome B
2 - Outcome D
3 - Outcome A
4 - Outcome C
Q4.
A toy brick that is dropped could land in one of four possible ways. Sofia drops the toy brick multiple times. How can Sofia improve her experiment to make it more accurate?
An image in a quiz
Drop the brick from different heights
Drop different bricks
Correct answer: Drop the brick more times
Drop the brick fewer times
Q5.
A dropped cone could land in one of two ways. The bar chart shows the results from an experiment. Which calculation shows how to find the experimental probability of the cone landing base down?
An image in a quiz
$$\frac{34+66}{34 \times66}$$
$$\frac{66-34}{66}$$
$$\frac{66}{66+34}$$
Correct answer: $$\frac{34}{66+34}$$
$$\frac{34}{66}$$
Q6.
A dropped cone could land in one of two ways. The bar chart shows the results from an experiment. In an experiment with 200 trials you should expect the cone to land base down times.
An image in a quiz
Correct Answer: 68