Probability
5.0 Data Handling and Probability · 5.2 Probability
Syllabus tag: Kenya CBC | Grade 8 Mathematics | Strand 5.0 Data Handling and Probability | Sub-Strand 5.2 Probability (7 lessons)
Lesson objectives
By the end of this sub-strand, you should be able to:
- Identify events involving chance in real-life situations
- Perform chance experiments and write the experimental probability outcomes
- Express probability outcomes as fractions, decimals, or percentages
Probability
Will it rain this afternoon? Will the bottle top land flat? Nobody knows for certain, but we can measure how likely each is.
Probability is that measurement. It is always a number between 0 and 1.
a) The scale
A probability of 0 means the event cannot happen. A probability of 1 means it must happen. Halfway along, the event is as likely as not.
No probability is ever below 0 or above 1. An answer of 1.4 means something has gone wrong.
b) Events involving chance
Some things are certain. The sun will set today.
Some are impossible. A goat will lay an egg.
Most sit between. Rain this afternoon. Picking a red bead. Scoring in the next match.
The word event simply means the thing we are watching for.
c) Doing an experiment
Some outcomes cannot be worked out by counting. A bottle top does not land flat and upside down with equal chance. No amount of thinking will tell you the split.
So we find out by trying. Toss it many times and record what happens. That is a chance experiment, and each toss is a trial.
d) Experimental probability
Divide the number of times the event happened by the number of trials.
The same answer can be written three ways. As a fraction, as a decimal, or as a percentage. All three mean exactly the same thing.
To go from fraction to decimal, divide. To go from decimal to percentage, multiply by 100.
e) More trials, better answer
Ten trials tell you very little. Five hundred tell you a great deal.
With few trials the result swings about. As trials increase, the experimental value settles closer to the true one.
This is why a fair test uses many trials. Two groups doing ten tosses each may report quite different answers.
f) Recording results
Use a tally chart. Mark each trial as it happens rather than trying to remember.
Count the total trials and check it matches how many you meant to do. A miscount changes every answer that follows.
g) Where this is used
A weather forecaster gives rain a percentage chance. A shopkeeper judges how much bread to stock. A farmer weighs the chance of the rains arriving on time before planting.
Words to know
- Probability -- a measure of how likely an event is to happen, ranging from 0 (impossible) to 1 (certain).
- Chance experiment -- an activity carried out to observe and record chance outcomes.
- Experimental probability -- probability calculated from the actual results of a chance experiment, rather than from known possible outcomes.
:::checkpoint Check yourself
- What does a probability of 0 mean?
- In 40 tosses a coin showed heads 18 times. What is the experimental probability?
- Write that answer as a decimal and as a percentage.
- Why is an experiment with 500 trials more trustworthy than one with 10? :::
Bridge to practice
Try the exercises below -- on chance events, experimental probability, and expressing probability as fractions, decimals, and percentages.