Probability
Probability tests classical probability from equally likely outcomes, complement rules, and simple combined events. The exam favours dice, cards, balls and spinners, with careful counting of the sample space.
Core rules
- P(E)=number of favourable outcomes/total number of equally likely outcomes.
- 0≤P(E)≤1; P(not E)=1−P(E); P(E)+P(E′)=1.
- For mutually exclusive events, P(E∪F)=P(E)+P(F).
- Two dice: 36 ordered outcomes; a card pack: 52 cards, 4 suits, 13 per suit.
- Without replacement, update both numerator and denominator after each draw.
- List equally likely outcomes systematically so that no outcome is omitted or repeated.
Worked example
A bag has 5 red and 3 blue balls. Two are drawn without replacement. P(both red)=5/8×4/7=20/56=5/14. P(at least one blue)=1−5/14=9/14.
Traps
Do not treat at least one as a single draw; use the complement. In without-replacement problems, the denominator changes. For two dice, (2,3) and (3,2) are different outcomes unless the question says otherwise. A probability greater than 1 signals a counting error.