Page 40 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 2 Probability
16. The complement rule: P(E) = 1 – P(E)

17. Two events are said to be exhaustive if it is certain that at least one of them occurs. If the events A
and B are exhaustive, then A  B = S.

18. Two or more events are mutually exclusive or disjoint if the events cannot occur at the same time.
19. If A and B are two mutually exclusive events, then
(a) A  B = φ, (b) P(A  B) = 0,
(c) P(A  B) = P(A) + P(B).
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20. If two events A and B are mutually exclusive and exhaustive, then
2 P(A  B) = 0 and P(A) + P(B) = 1

21. An event and its complement are always exhaustive and mutually exclusive:
P(A  A) = 1 as well as P(A  A) = 0

22. Addition rule of probability: S
P(A  B) = P(A) + P(B) – P(A  B) A B

23. Conditional probability
The probability of event A happening given that event B has happened,
P(A | B) = P(A  B) , provided that P(B) ≠ 0.
P(B)

24. Multiplication rule of probability: P(A  B) = P(A | B) × P(B)
25. P(A | B) × P(B) = P(B | A) × P(A)

26. If A and B are mutually exclusive events, i.e. A  B = φ, then P(A  B) = 0. Thus,
P(A | B) × P(B) = P(B | A) × P(A) = 0
27. For mutually exclusive and exhaustive events A and A, A  A = φ, A  A = S,
(a) P(S | B) = P(A | B) + P(A | B)
(b) P(S | B) = 1
(c) P(A | B) + P(A | B) = 1
.
.
28. P(A) = P(A | B) P(B) + P(A | B) P(B)
29. If the outcome of event A does not affect the outcome of event B, then A and B are independent

30. If events A and B are independent, then
(a) P(A | B) = P(A) or, equivalently P(B | A) = P(B).
(b) P(A  B) = P(A) × P(B)

31. The rule of total probability states that: if {A , A , …, A } is a partition of S such that
1 2 k
k
P(A) . 0 for i = 1, 2, …, k, then for any event B, P(B) = ∑ P(A)P(B | A)
i i i
i = 1

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02 STPM Math(T) T3.indd 108 28/10/2021 10:21 AM