Experimental probability.pptx

EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Experimental probability

Probability

Lesson 3 of 6

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Warm-up

Probability

Lesson 3 of 6

Answer each one, then check.

1

Simplify 30/120.

2

Write 18/60 as a decimal.

3

What is the theoretical probability of heads on a fair coin?

4

Work out 500 × 0.3.

5

What is 1/6 as a decimal, to 2 decimal places?

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Warm-up - Answers

Probability

Lesson 3 of 6

1

Simplify 30/120.

¼

2

Write 18/60 as a decimal.

0.3

3

What is the theoretical probability of heads on a fair coin?

½

4

Work out 500 × 0.3.

150

5

What is 1/6 as a decimal, to 2 decimal places?

0.17

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Learning Objectives

Probability

Lesson 3 of 6

1

Work out relative frequency.

2

Use relative frequency to estimate probability.

3

Predict how many times an event will happen.

4

Decide whether a coin, dice or spinner is fair.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Probability

Lesson 3 of 6

RELATIVE FREQUENCY

Relative frequency is the number of times an event happens divided by the total number of trials.

relative frequency = (frequency of the event)/(total number of trials)

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Relative Frequency Settles Down

Probability

Lesson 3 of 6

The more trials, the closer the relative frequency gets to the true probability.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Relative Frequency

Probability

Lesson 3 of 6

A spinner is spun 60 times. It lands on red 18 times, blue 30 times and green 12 times. Find the relative frequency of each colour.

1

Red

18/60 = 0.3

2

Blue

30/60 = 0.5

3

Green

12/60 = 0.2

ANSWER

Red 0.3, blue 0.5, green 0.2. These add up to 1.

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Predicting Outcomes

Probability

Lesson 3 of 6

Use the spinner results to estimate how many times you would expect blue in 500 spins.

1

Estimated probability of blue

0.5

2

Multiply by the number of spins

0.5 × 500 = 250

ANSWER

About 250 blues.

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Is the Dice Fair?

Probability

Lesson 3 of 6

A dice is rolled 120 times and lands on 6 a total of 30 times. Does this suggest the dice is biased?

1

Relative frequency of a 6

30/120 = 0.25

2

Expected for a fair dice

1/6 = 0.167, so about 20 sixes

3

Compare

30 is much bigger than 20

ANSWER

The relative frequency 0.25 is well above 1/6, which suggests the dice may be biased, but more trials would give a more reliable conclusion.

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Theoretical or Experimental?

Probability

Lesson 3 of 6

THEORETICAL PROBABILITY

• Worked out from equally likely outcomes.

• Example: P(head) = ½.

• Does not change.

EXPERIMENTAL PROBABILITY

• Estimated from the results of trials.

• Example: 18 heads in 40 tosses gives 0.45.

• Changes as you do more trials.

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How Reliable Is an Estimate?

Probability

Lesson 3 of 6

More trials give better estimates.

Small samples

10 tosses might give 7 heads: 0.7 is a poor estimate of 0.5.

Large samples

1000 tosses will usually give a relative frequency very close to 0.5.

Fair

A fair dice or coin should give relative frequencies close to the theoretical values.

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Key Terms

Probability

Lesson 3 of 6

Trial

One repeat of an experiment.

Frequency

How many times an outcome happens.

Relative frequency

Frequency divided by the number of trials.

Theoretical probability

The probability worked out from equally likely outcomes.

Expected number

Probability multiplied by the number of trials.

Fair

Every outcome is equally likely.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Probability

Lesson 3 of 6

YOUR TASK

Coin Toss Experiment

15 minutes

Toss a coin 10 times and record the number of heads. Combine class results in groups of 10, 50 and 100 tosses. Work out the relative frequency of heads for each total and comment on how close each is to 0.5.

1

Collect results.

2

Combine.

3

Compare.

WHAT A GOOD ANSWER SHOWS

Small groups vary widely (for example 3 or 7 heads out of 10), while the combined class total is very close to 0.5. This shows that relative frequency settles as the number of trials grows.

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Can I...?

Probability

Lesson 3 of 6

Work out relative frequency.

Use it as an estimate of probability.

Work out an expected number.

Compare experimental and theoretical results.

Say whether a dice looks fair.

Explain why more trials are better.

Show relative frequencies add to 1.

Draw a relative frequency graph.

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Summary & Exam Focus

Relative frequency = frequency/trials.

Expected number = probability × trials.

More trials give a more reliable estimate.

Compare with the theoretical probability to test fairness.

EXAM FOCUS

A spinner is spun 200 times. It lands on red 62 times. Work out an estimate for the probability that it lands on red, and how many reds you expect in 500 spins. (3 marks)

Relative frequency is frequency divided by the number of trials. Multiply by the number of spins for the expected number.

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