Probability of Combined Events · Form 4
Probability of Combined Events: Worked Examples (Easier)
Builds confidence with the basics: writing the sample space, finding the probability of a single event, and using the complement (1 − P). Good for students starting Form 4 probability.
Worked example 1
A bag contains 3 red, 4 blue and 5 green marbles. One marble is drawn at random.
Find the probability that it is green.
- Count all outcomes: 3 + 4 + 5 = 12 marbles.
- Favourable outcomes (green) = 5.
- P(green) = number of green ÷ total = 5/12.
Worked example 2
A fair die is rolled once. Find the probability of not getting a '4'.
- Sample space = {1, 2, 3, 4, 5, 6}, so P(4) = 1/6.
- Use the complement: P(not 4) = 1 − P(4).
- = 1 − 1/6 = 5/6.
Worked example 3
A card is drawn at random from cards, each showing one letter of the word 'MATEMATIK'. Find the probability that the letter is 'A'.
- Count all letters in MATEMATIK: M-A-T-E-M-A-T-I-K = 9 letters.
- Count the letter 'A': it appears 2 times.
- P(A) = 2/9.
Worked example 4
A spinner is divided into 8 equal sections. Three sections are labelled X and five are labelled Y.
The spinner is spun once. Find the probability that it stops on X.
- Number of X sections = 3; total sections = 8.
- P(X) = number of X sections ÷ total sections.
- P(X) = 3/8.
Worked example 5
A fair six-sided die is rolled once. Find the probability of getting an even number.
- Even numbers on a die: 2, 4, 6 → 3 outcomes.
- Total outcomes = 6.
- P(even) = 3/6 = 1/2.
Worked example 6
A card is drawn at random from ten cards numbered 1 to 10. Find the probability that the number on the card is a prime number.
- Prime numbers from 1 to 10: 2, 3, 5, 7 → 4 primes.
- Total cards = 10.
- P(prime) = 4/10 = 2/5.
Worked example 7
A box contains 6 pens: 2 blue, 3 black and 1 red. A pen is chosen at random from the box.
Find the probability that it is black.
- Total number of pens = 2+3+1 = 6
- Number of black pens = 3
- P(black) = 3/6 = 1/2
Worked example 8
A fair spinner has 10 equal sections numbered 1 to 10. The spinner is spun once.
Find the probability that it does NOT stop on a multiple of 3.
- Multiples of 3 from 1 to 10: 3, 6, 9 → there are 3 of them
- P(multiple of 3) = 3/10
- P(not a multiple of 3) = 1 − 3/10 = 7/10
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
What's actually tested at the easy level for combined events?
Easy questions check whether you can tell independent events (like tossing two coins) apart from mutually exclusive events (like picking a red or blue ball in one draw), then apply the right rule, multiply for "and", add for "or". You'll also draw simple probability trees for two events.
How do I know when to add probabilities and when to multiply them?
Multiply when both events must happen together (an "and" situation, usually two separate actions like two spins). Add when only one of several outcomes can happen (an "or" situation from a single action), but only if the events are mutually exclusive, otherwise you must subtract the overlap first.
What mistakes cost marks in easy combined-events questions?
Students often add probabilities when they should multiply, or forget that mutually exclusive events cannot happen at the same time (so P(A and B) = 0). Another common slip is leaving a probability as an unsimplified calculation instead of reducing the fraction, which examiners expect in the final answer.