Topic 10 of 11 · Form 2
Probability
P(event) = number of favourable outcomes ÷ total equally likely outcomes; 0 ≤ P ≤ 1; P(not A) = 1 − P(A). Relative frequency estimates probability from experiments; expected frequency = P × number of trials.
Notes for this topic 1 file, in order
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Basic probability
P(event) = number of favourable outcomes ÷ total equally likely outcomes; 0 ≤ P ≤ 1; P(not A) = 1 − P(A). Relative frequency estimates probability from experiments; expected frequency = P × number of trials.
Combined events
- Sample space diagrams and two-way tables.
- Tree diagrams: multiply along branches, add between outcomes.
- Independent events: P(A and B) = P(A) × P(B).
- Mutually exclusive events: P(A or B) = P(A) + P(B).
- Without replacement: probabilities change on the second branch.
Worked example: A bag has 5 red and 3 blue balls. Two are taken without replacement. Find P(both red) and P(one of each colour).
P(RR) = 5/8 × 4/7 = 20/56 = 5/14
P(RB or BR) = 5/8 × 3/7 + 3/8 × 5/7 = 30/56 = 15/28
Venn diagrams
Show sets and their overlaps; P(A ∪ B) = P(A) + P(B) − P(A ∩ B). Conditional probability from tables or Venn diagrams.
Check yourself
- A fair die is rolled 120 times. How many sixes are expected?
- P(rain) = 0.3. Find P(no rain).
- Two coins are tossed. Find P(two heads).
Show answers
- 20
- 0.7
- ¼
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