top of page

13.3 Experimental Probability

GCSE Maths Foundation · Edexcel · Chapter 13: Probability

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: relative frequency, expected outcomes, and deciding whether something is fair. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

  • Work out relative frequency from the results of an experiment
  • Explain why more trials give a more reliable estimate of probability
  • Work out how many times you expect an outcome to happen
  • Use results to decide whether a dice, coin or spinner is likely to be fair or biased

Key words

  • Trial: One go at an experiment, for example one throw of a dice.
  • Relative frequency: The fraction of trials in which an outcome happened. It is an estimate of the probability.
  • Expected outcomes: How many times you would expect an outcome in a given number of trials: probability × number of trials.
  • Fair: All outcomes are equally likely.
  • Biased: Not fair: some outcomes are more likely than others.

Relative frequency

Some probabilities cannot be worked out by counting equally likely outcomes, for example a drawing pin landing point up. Instead we do an experiment and use the results.

Key fact: Relative frequency = number of times the outcome happens ÷ total number of trials

Worked example: a drawing pin

A drawing pin is thrown 200 times. It lands point up 64 times.
Relative frequency of point up = 64/200 = 0.32.
So an estimate of P(point up) is 0.32, and of P(point down) is 1 − 0.32 = 0.68.

Answer: 0.32

More trials give a better estimate

With only a few trials the relative frequency jumps about. As the number of trials grows, it settles down. So the estimate from the most trials is the most reliable. You can also combine everyone’s results.

Worked example: combining results

Leah throws a pin 50 times: 18 point up. Omar throws it 150 times: 46 point up.
Omar’s estimate is more reliable because he did more trials.
The best estimate uses all 200 throws: (18 + 46)/200 = 64/200 = 0.32.

Answer: 0.32

Expected outcomes

Key fact: Expected number = probability × number of trials

Worked example: a fair dice

A fair dice is rolled 150 times. How many sixes would you expect?
1/6 × 150 = 150 ÷ 6 = 25.

Answer: 25 sixes

Worked example: using a relative frequency

In a survey, 18 out of 60 shoppers paid with cash. Estimate how many of 1500 shoppers pay with cash.
Relative frequency = 18/60 = 0.3. 0.3 × 1500 = 450.

Answer: about 450 shoppers

The expected number is what happens on average. The real result will usually be close to it but not exactly equal.

Fair or biased?

Compare the results with what you would expect if the object were fair. A small difference is normal. A big difference over a large number of trials suggests bias.

  • Frequency; 1 47; 2 52; 3 49; 4 81; 5 35; 6 36

Worked example: is the dice fair?

The table shows 300 rolls of a dice. For a fair dice we expect 300 ÷ 6 = 50 of each score.
A score of 4 came up 81 times. That is far more than 50 over a large number of rolls.
Relative frequency of 4 = 81/300 = 0.27, compared with 1/6 ≈ 0.17.

Answer: The dice is probably biased towards 4.

Note: With only a few trials (say 6 or 10) you cannot tell whether something is biased – there are not enough results.

Common mistakes

  • Dividing by the wrong total. Relative frequency uses the total number of trials.
  • Saying a dice is biased after only a few rolls. You need lots of trials.
  • Expecting the real result to equal the expected number exactly.
  • Choosing the estimate from the person with the fewest trials. More trials means more reliable.

Revision questions

Try these, then check your answers below each one.

Question 1. A coin is flipped 150 times and lands on heads 69 times. Work out the relative frequency of heads.

Answer: 0.46

Working: 69/150 = 0.46.

Question 2. A fair dice is rolled 300 times. How many times would you expect to roll a 3?

Answer: 50

Working: 1/6 × 300 = 50.

Question 3. Four students each throw the same drawing pin. Whose results give the most reliable estimate of the probability of it landing point up? (Choose from: Ali: 10 throws, Bea: 50 throws, Cy: 100 throws, Di: 1000 throws.)

Answer: Di: 1000 throws

Working: Di did the most trials, so Di’s relative frequency is the most reliable estimate.

Related lessons

Continue in the full course

This lesson is section 13.3 (EGCMF1303) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.

 

 

 

 

 

 

 

bottom of page