Skip to content
Request a demo

Grade 10 · Core Mathematics · Lesson 1 of 12

Performing Probability Experiments and Finding Experimental Probability

A Grade 10 Core Mathematics CBE lesson from the sub-strand Probability 1. In it, learners perform probability experiments using a fair die and record outcome frequencies.

Strand Statistics and ProbabilitySub-strand Probability 1Lesson code 10CM-32-L140 minutes · 3 slides

KICD learning outcome (a)

Perform experiments involving probabilities in different situations.

By the end of this lesson, learners should be able to

  1. Perform probability experiments using a fair die and record outcome frequencies.
  2. Calculate experimental probability as the ratio of favourable outcomes to total outcomes.
  3. Compare experimental results from repeated trials against expected theoretical probabilities.

Key vocabulary

Experimental Probability
The likelihood of an outcome calculated from the recorded results of an experiment.
Rolling a 4 five times in 25 tosses gives an experimental probability of 5/25.
Relative Frequency
The fraction of times a specific result occurs out of total performed trials.
If face 2 appears 6 times in 25 rolls, its relative frequency is 6/25.
Favourable Outcome
A targeted result in an experiment that satisfies a specified event condition.
Obtaining an even number on a die roll is a favourable outcome here.
Trial
A single performance or observation within a probability experiment or testing procedure.
Each roll of the fair die represents one individual experimental trial.
Frequency Table
A structured grid displaying outcomes alongside their counted number of occurrences.
The frequency table lists each die face and how often it occurred.
Empirical Data
Information gained by direct observation or physical experiment rather than theoretical deduction.
We calculated the experimental probability directly from our empirical data.

Lesson preview

Slide 1 · Conducting Probability Experiments with a Six-Sided CubeOpening · 12 min
A bar chart displaying the frequency of each face obtained after rolling a six-sided die 25 times.
Figure 1: A bar chart displaying the frequency of each face obtained after rolling a six-sided die 25 times.

In this intro experiment, we perform practical trials by throwing a standard six-sided die 25 times and recording every outcome. By collecting empirical data across multiple rolls, we tally how frequently each face turns up in a simple summary grid. Dividing the tally count of each outcome by 25 gives its relative frequency. We then compare our observed frequencies with expected theoretical outcomes and analyse differences across various group findings. Use Figure 1 to see how observed frequencies from our trials can be visually summarised.

  • Conducting probability experiments allows us to collect real trial counts across repeated physical attempts.
  • In our first experiment, we roll a six-sided die 25 times to observe actual outcome frequencies.
  • Divide each outcome frequency by 25 to obtain the corresponding relative frequency value.
  • Compare observed experimental ratios with expected theoretical values and share findings across different student pairs.
Worked example. Step 1: Write down the total number of tosses made, which is 25. Step 2: Divide the frequency of Face 3 by 25: 625=0.24. Step 3: Divide the frequency of Face 5 by 25: 425=0.16. Answer: The relative frequency for Face 3 is 625 (0.24) and for Face 5 is 425 (0.16)..

Check question: If a six-sided cube is rolled 25 times and face 6 appears 5 times, what is the relative frequency of face 6?

  1. 0.2
  2. 0.24
  3. 5
  4. 0.8
Show answer

0.2. The relative frequency is obtained by dividing the frequency of the outcome (5) by the total number of trials (25), yielding 525=0.2.

Slide 2 · Calculating Experimental Probability from Frequency DataModel · 14 min
A table showing the calculation of experimental probabilities as simplified fractions for 50 tosses of a six-sided die.
Figure 2: A table showing the calculation of experimental probabilities as simplified fractions for 50 tosses of a six-sided die.

Teach the full lesson on the projector

This lesson, and every other Grade 1–10 CBE lesson, comes ready to project with the EAP ClassKit. It runs without electricity or internet.

  • All 3 slides with diagrams and class activities
  • Teacher notes, SNE adaptations and assessment checks
  • Homework and the other 11 lessons in this sub-strand
See the school projectorWhatsApp us

All 12 lessons in Probability 1

  1. 1Performing Probability Experiments and Finding Experimental ProbabilityPerform experiments involving probabilities in different situations
  2. 2Empirical Probabilities and Experimental InvestigationsPerform experiments involving probabilities in different situations
  3. 3Identifying Range of Probability and Complementary EventsIdentify the range of probability in different situations
  4. 4Generating Probability Space of EventsGenerate probability space of different events
  5. 5Generating Probability Space for Compound EventsGenerate probability space of different events
  6. 6Determining Probability of Mutually Exclusive Events and Introduction to Independent EventsDetermine the probability of mutually exclusive events and independent events
  7. 7Determining Probability of Independent Events and Multi-Stage SelectionsDetermine the probability of mutually exclusive events and independent events
  8. 8Probability Bounds, Complementary Events, and the Addition LawApply the laws of probability in different situations
  9. 9Applying Laws of ProbabilityApply the laws of probability in different situations
  10. 10Determining Probability of Independent Events Using Tree DiagramsDetermine the probability of independent events using tree diagrams
  11. 11Tree Diagrams for Multi-Stage Independent EventsDetermine the probability of independent events using tree diagrams
  12. 12Applications of Probability in Real-Life ContextsAppreciate the application of probability in real-life situations