Probability
This domain tests classical probability for simple events, complementary events, and standard experiments with coins, dice and cards.
Core rules
- P(E) = number of favourable outcomes / total number of equally likely outcomes.
- 0 ≤ P(E) ≤ 1; P(not E) = 1 − P(E).
- The sum of probabilities of all elementary outcomes is 1.
- A standard die has 6 outcomes; two dice have 36 ordered outcomes; a standard deck has 52 cards with 4 suits and 13 cards per suit.
- At least one is often handled by the complement: P(at least one) = 1 − P(none).
- The sample space is the set of all possible outcomes; an event is a subset of it.
Worked example
Two fair dice are rolled once. Find the probability that the sum is 8. Total outcomes = 6 × 6 = 36. Favourable outcomes: (2,6), (3,5), (4,4), (5,3), (6,2), five outcomes in all. P(sum 8) = 5/36. The complementary probability is P(sum ≠ 8) = 31/36, and the two add to 1.
Traps
- Treating (2,6) and (6,2) as one outcome on two dice.
- Miscounting the total when a card is drawn and replaced or not replaced.
- Confusing at least one with exactly one.
- Reporting a probability greater than 1 after using counts without dividing by the total.