1
Independent vs Dependent
The occurrence of one event affecting the other:
- Independent (Tak Bersandar): Outcome of event $A$ does not affect $B$. (e.g. Tossing 2 coins, sampling with replacement).
$$P(A \cap B) = P(A) \times P(B)$$
- Dependent (Bersandar): Outcome of event $A$ alters probabilities of $B$. (e.g. Drawing marbles without replacement).
2
Mutually Exclusive Events
Events that cannot occur simultaneously ($A \cap B = \emptyset$):
$$P(A \cup B) = P(A) + P(B)$$
Non-mutually exclusive: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.
3
Complement of an Event
Probability of event $A$ NOT happening ($A'$):
$$P(A') = 1 - P(A)$$
Useful for questions asking for *"at least one"* ($\text{At least 1} = 1 - P(\text{none})$).
SPM Secret: "Without Replacement" (Tanpa Pengembalian)
In SPM Paper 2, always check if items are returned or not! If a bag has 3 Red and 5 Blue marbles (Total 8), picking a Red marble first leaves only 2 Red and 7 Total marbles. The second probability becomes $\frac{2}{7}$, NOT $\frac{3}{8}$! Students frequently lose all accuracy marks by forgetting to decrease the denominator.