Grade 9 Probability: Short Notes

9 ශ්‍රේණිය · 24 පරිච්ඡේදය · සම්භාවිතාව

45%

of Grade 9 term tests include it (18 of 40)

159

marks in past papers (24 questions)

9 min

full lesson with quick checks

🎯 What you'll learn

Recognise a random experiment and its features
Write the sample space of an experiment and find n(S)
Decide whether the outcomes are equally likely
Find P(A) = n(A)/n(S) for an event A
Use P(A') = 1 − P(A) and work backwards from a probability

Waiting for a six

In Ludo you need a 6 to bring a piece out. Your little brother says he has a fifty-fifty chance: 'either it's a 6 or it isn't'. Is he right? By the end of this lesson you can give the exact chance, and show him why he's wrong.

Random experiments

Rolling a die is a random experiment:• you know every possible result before you start;• you can't say which result you'll get on a particular try;• you can repeat it as often as you like;• the results show no pattern, however many times you repeat it.Tossing a coin, drawing a chit for a prize and spinning a spinner are random experiments too.

The sample space

The set of all possible outcomes is the sample space, S. n(S) is the number of outcomes.• Coin: S = {H, T}, n(S) = 2• Die: S = {1, 2, 3, 4, 5, 6}, n(S) = 6• A letter chosen from the word KANDY: S = {K, A, N, D, Y}, n(S) = 5

Equally likely or not?

On the left, the four sectors are equal, so 1, 2, 3 and 4 are equally likely. On the right, sector 1 is half the circle, so 1 is more likely than 2 or 3.

Events

An event is a subset of the sample space: the outcomes you are interested in.Rolling a die, the event 'an even number' is A = {2, 4, 6}, so n(A) = 3.The event 'a number greater than 4' is B = {5, 6}, so n(B) = 2.

🧮 Probability of an event

Use it only when the outcomes are equally likely. n(A) is the number of outcomes in the event, n(S) the number in the sample space.

P(A) = n(A) / n(S)

✏️ Back to Ludo

A fair die is rolled. Find the probability of (i) getting a 6 (ii) getting a prime number.

1S = {1, 2, 3, 4, 5, 6}, n(S) = 6. The die is fair, so outcomes are equally likely.
2(i) A = {6}, so P(A) = 1/6. Not ½: there are six equally likely outcomes, not two.
3(ii) Primes: B = {2, 3, 5}. 1 is not prime.
4P(B) = 3/6 = 1/2

✅ (i) 1/6 (ii) 1/2

From 0 to 1, and 'not A'

Every probability is between 0 and 1.• An impossible event has probability 0 (a 7 on a die).• A certain event has probability 1 (a number less than 7).The event 'A does not happen' is the complement, A'. Since A and A' share out all the outcomes:P(A') = 1 − P(A)

✏️ Numbered chits

Twenty chits numbered 1 to 20 are in a box. One is drawn at random. Find the probability that the number is (i) a multiple of 3 (ii) not a multiple of 3.

1n(S) = 20
2A = {3, 6, 9, 12, 15, 18}, n(A) = 6
3(i) P(A) = 6/20 = 3/10
4(ii) P(A') = 1 − 3/10 = 7/10

✅ (i) 3/10 (ii) 7/10

⚠️ Divide by the total, not by the rest

With 3 coffee toffees and 9 others, some students write P = 3/9. That compares coffee with 'not coffee'. The bottom number is always n(S), the total: 3/12.Also count carefully: list the outcomes in a set before counting, and remember 1 is not a prime number.

⚠️ Two outcomes doesn't mean ½

'A 6 or not a 6' is two results, but they are not equally likely: 'not a 6' covers five faces. Always count the equally likely outcomes in S.P(6) = 1/6 and P(not 6) = 5/6. So the little brother in the Ludo game was wrong.

📌 Remember

• Sample space S = all possible outcomes; n(S) counts them.• An event is a subset of S.• For equally likely outcomes: P(A) = n(A)/n(S).• 0 ≤ P(A) ≤ 1; impossible = 0, certain = 1.• P(A') = 1 − P(A). Always divide by the total.

🧾 Quick revision sheet

What is a sample space?	The set of all possible outcomes of a random experiment.
Sample space for rolling a die	S = {1, 2, 3, 4, 5, 6}, n(S) = 6
What is an event?	A subset of the sample space.
Probability of an event A (equally likely outcomes)	P(A) = n(A)/n(S)
Probability of an impossible event, and of a certain event	0 and 1
P(A') when P(A) = 2/7	1 − 2/7 = 5/7

Now test yourself: 4 quick checks and 1 more worked examples

The full lesson checks your answers as you go, and Gedara Sir tracks which parts you've got.

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