Probability
This section covers Probability. The exam tests classical probability with equally likely outcomes, complementary events, and standard experiments such as dice, coins, and cards.
Core rules
- For equally likely outcomes, P(E) = number of favourable outcomes / total number of outcomes.
- 0 ≤ P(E) ≤ 1. P(impossible event) = 0; P(sure event) = 1.
- Complement rule: P(not E) = 1 - P(E).
- For a die, total outcomes = 6; for two coins, total outcomes = 4; for a standard deck, total cards = 52, with 4 suits and 13 cards per suit.
- When drawing without replacement, reduce both favourable and total counts after each draw.
Worked example
A die is rolled once. The even outcomes are 2, 4, 6, so P(even) = 3/6 = 1/2. A card is drawn from a standard deck. There are 4 kings, so P(king) = 4/52 = 1/13. The probability of not drawing a king is 1 - 1/13 = 12/13.
Traps
Do not count outcomes that are not equally likely as if they were. “At least one” is often easier through the complement. In card problems, remember that aces and face cards are separate categories. For two dice, there are 36 ordered outcomes, not 21 sums. Always check that the probability lies between 0 and 1.