Last reviewed: 10 November 2026
Updated November 2026. These Grade 9 probability notes explain experiments with equally likely outcomes, the range of probability, mutually exclusive events, independent events and simple tree diagrams. Probability measures how likely an event is, on a scale from 0 (impossible) to 1 (certain). When all outcomes are equally likely, the probability of an event is the number of favourable outcomes divided by the total number of outcomes. For example, the probability of rolling a 4 on a fair die is 1/6.
The examples and questions are original practice for Kenyan junior school learners, not an official paper. For the other Grade 9 maths topics, see our Grade 9 maths revision guide and the Grade 9 notes hub.
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What the Grade 9 Curriculum Covers
Probability is a sub-strand under Data Handling and Probability in the Kenya Institute of Curriculum Development’s Grade 9 Mathematics design. Learners perform experiments with equally likely outcomes, find the range of probability of an event, identify mutually exclusive events, perform experiments with independent events, and draw tree diagrams. The design also mentions avoiding harmful practices such as gambling. It is listed on the KICD Grade Nine curriculum designs page.
Key Words
These terms follow OpenStax Introductory Statistics’ probability terminology.
- Experiment: an action with uncertain results, such as tossing a coin.
- Outcome: one possible result, such as heads.
- Sample space: the list of all possible outcomes. For one die it is {1, 2, 3, 4, 5, 6}.
- Event: one or more outcomes, such as “an even number”.
The Range of Probability
Every probability lies between 0 and 1 inclusive. An impossible event, such as rolling a 7 on an ordinary die, has probability 0. A certain event, such as rolling a number less than 7, has probability 1. Probabilities can be written as fractions, decimals or percentages: 1/4 = 0.25 = 25%. If the probability that an event happens is p, the probability that it does not happen is 1 − p.
Worked example: equally likely outcomes
A bag has 3 red, 5 blue and 2 green counters, all the same size. One is picked without looking. P(blue) = 5/10 = 1/2. P(not green) = 1 − 2/10 = 8/10 = 4/5. P(yellow) = 0, since there are no yellow counters.
Experimental probability
If you toss a coin 50 times and get 27 heads, the experimental probability of heads is 27/50 = 0.54. With more tosses, the experimental value for a fair coin tends to get closer to 1/2. Recording results in a class experiment is a good way to see this.
Mutually Exclusive Events
Events are mutually exclusive if they cannot happen at the same time. On one roll of a die, “getting a 2” and “getting a 5” are mutually exclusive. For mutually exclusive events, P(A or B) = P(A) + P(B), as set out in OpenStax’s section on independent and mutually exclusive events. So P(2 or 5) = 1/6 + 1/6 = 1/3.
“Getting an even number” and “getting a number greater than 3” are not mutually exclusive, because 4 and 6 belong to both. Adding their probabilities would count 4 and 6 twice.
Independent Events
Events are independent if one does not affect the probability of the other, such as tossing a coin and rolling a die. For independent events, P(A and B) = P(A) × P(B). P(heads and a 6) = 1/2 × 1/6 = 1/12.
Tree Diagrams
A tree diagram shows outcomes as branches. Write the probability on each branch, multiply along a path for “and”, and add the end results of different paths for “or”.
Worked example: two coin tosses
First toss: H (1/2) or T (1/2). From each, the second toss branches into H (1/2) or T (1/2). The four paths are HH, HT, TH and TT, each with probability 1/2 × 1/2 = 1/4. P(exactly one head) = P(HT) + P(TH) = 1/4 + 1/4 = 1/2. Check: all four paths add to 1.
A note on games of chance
Probability explains why betting is a poor way to make money: the odds in commercial games are set so that, over many plays, the operator expects to collect more than it pays out. Understanding this is one of the real-life uses the curriculum points to.
Original Practice Questions With Worked Answers
- A fair die is rolled. Find P(a number less than 3). {1, 2}: 2/6 = 1/3.
- The probability it rains tomorrow is 0.35. What is the probability it does not? 1 − 0.35 = 0.65.
- A card is drawn from 10 cards numbered 1 to 10. Find P(3 or 8). Mutually exclusive: 1/10 + 1/10 = 1/5.
- A coin is tossed and a die rolled. Find P(tails and an odd number). 1/2 × 3/6 = 1/4.
- Two coins are tossed. Find P(two tails). 1/2 × 1/2 = 1/4.
- Can a probability be 1.2? No. Probabilities are never greater than 1.
Cover the answers and attempt each question first. For timed practice, use the Grade 9 revision papers or the Grade 9 CBC Challenge. These notes are free; full revision access is available with the KSh 20 Day Pass or the KSh 500 Monthly Pass.
Frequently Asked Questions
What is the range of probability?
From 0 to 1. A probability of 0 means the event is impossible and 1 means it is certain.
What are mutually exclusive events?
Events that cannot happen at the same time, such as rolling a 1 and rolling a 6 on a single throw of a die. Their probabilities can be added.
What are independent events?
Events where the result of one does not change the probability of the other, such as tossing a coin and rolling a die. Their probabilities are multiplied.
How do you use a tree diagram?
Write probabilities on the branches, multiply along each path to find the probability of that combination, and add paths when more than one combination gives the event you want.