New
New
Year 11
Higher

Experimental vs theoretical probability

I can see the impact of sample size and compare theoretical probabilities to experimental ones.

New
New
Year 11
Higher

Experimental vs theoretical probability

I can see the impact of sample size and compare theoretical probabilities to experimental ones.

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Lesson details

Key learning points

  1. Different sample sizes can impact the experimental probabilities
  2. As the sample size increases, the experimental probabilities approach the theoretical probabilities
  3. A larger sample size is more likely to show a truer estimation of the underlying probability

Keywords

  • Trial - A trial is a single, pre-defined test.

  • Experiment - An experiment is a repetition of a trial multiple times in order to observe how often each outcome occurs.

  • Probability - The probability that an event will occur is the proportion of times the event is expected to happen in a suitably large experiment.

Common misconception

Pupils may assume that it possible to determine whether a coin (or other object/game) is biased by conducting an experiment with a small number of trials.

The greater the number of trial that an experiment contains, the closer the relative frequency of an outcome gets to its theoretical probability.

Aspects of the lesson can be made practical by replicating some of the experiments in the classroom (e.g. Andeep's puzzle to work out how many counters of each colour are in a box). The lesson also contains some links to Desmos files which can be used to simulate 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.
__________ probability can be determined by the number of times an event occurred during multiple trials.
A biased
Correct answer: An experimental
A fair
A theoretical
Q2.
Select the fair spinners.
An image in a quiz
Correct Answer: 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. Jun 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 D
2 - Outcome B
3 - Outcome C
4 - Outcome A
Q4.
A toy brick that is dropped could land in one of four possible ways. Sofia and Jun drop the toy brick multiple times. Whose results should be the most reliable? Why?
An image in a quiz
Correct answer: Sofia's results
Jun's results
Correct answer: Sofia has carried out more trials.
Jun has carried out fewer trials.
Jun's results look more consistent.
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 curve down?
An image in a quiz
$$\frac{34}{66}$$
$$\frac{34}{66+34}$$
Correct answer: $$\frac{66}{66+34}$$
$$\frac{66-34}{66}$$
$$\frac{34+66}{34 \times66}$$
Q6.
A dropped cone could land in one of two ways. The bar chart shows the results from an experiment. In an experiment with 800 trials you should expect the cone to land curve down times.
An image in a quiz
Correct Answer: 528

6 Questions

Q1.
In which of these situations is it possible to work out a theoretical probability?
Predicting the winner in a game of chess
Correct answer: Predicting the outcome of flipping a fair coin
Predicting which way up a toy brick lands
Correct answer: Predicting the outcome of flipping a fair die
Predicting the winner in a race
Q2.
Alex flips a coin 4 times. The coin lands heads 3 times. Which of these statements are correct?
The coin is definitely biased towards heads.
The coin is definitely not biased towards heads.
Correct answer: The coin could be biased towards heads but more trials are needed to be sure.
Correct answer: The coin could be fair but more trials are needed to be sure.
The coin is definitely fair.
Q3.
A spinner contains three letters: A, B and C. The tables show results from four experiments with the spinner. Which experiment will produce the most reliable set of experimental probabilities?
An image in a quiz
Experiment 1
Experiment 2
Experiment 3
Correct answer: Experiment 4
Q4.
The table shows the theoretical probabilities of taking a counter of a particular colour out of a bag of counters. In 1000 trials the number of times you should expect to draw a blue counter is .
An image in a quiz
Correct Answer: 450
Q5.
A box contains 400 counters. A counter is drawn, its colour noted and replaced. The results are in the table. Estimate how many red counters are in the box.
An image in a quiz
28.5
57
86
Correct answer: 114
228
Q6.
A class investigates whether a 6-sided die is biased. The table shows the results. Estimate the probability of the die landing on a prime number. P(prime) = (as an unrounded decimal).
An image in a quiz
Correct Answer: 0.5025