ZIMSEC O Level · Mathematics · Form 3, Form 4
Probability measures how likely an event is, on a scale from 0 (impossible) to 1 (certain).
Basic rules
- P(event) = number of favourable outcomes ÷ total number of equally likely outcomes.
- P(not A) = 1 − P(A).
- Mutually exclusive events (cannot happen together): P(A or B) = P(A) + P(B).
- Independent events (one does not affect the other): P(A and B) = P(A) × P(B).
Worked example: A bag has 5 red and 3 blue beads. One bead is taken at random. Find P(blue).
P(blue) = 3 ÷ 8
Two events
Use a sample space (table of outcomes) or a tree diagram. Multiply along branches; add the end results that you need.
Worked example: Two beads are taken from the same bag without replacement. Find P(both red).
P(red then red) = 5/8 × 4/7 = 20/56 = 5/14
Exam tip: “Without replacement” means the total (and possibly the number of that colour) goes down by one for the second pick.
Check yourself
- A fair die is thrown. Find P(a number greater than 4).
- The probability that it rains tomorrow is 0.3. Find the probability that it does not rain.
- A coin is tossed and a die is thrown. Find P(head and a 6).
Show answers
- 2/6 = 1/3
- 0.7
- ½ × 1/6 = 1/12
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