Page 20 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 2 Probability
Note: If events A and B are not only exhaustive but they are also mutually exclusive, then exactly one of
the events can happen. For instance, an event and its complement are always exhaustive and mutually
exclusive:

P(A  A) = 1 as well as P(A  A) = 0.

Example 22

A fair die is tossed, let event A = obtain a one,
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event B = obtain a four,
event C = obtain an even number,
2 event D = obtain an odd number.
Which of the following groups of events are mutually exclusive?
(a) A and B (b) B and C (c) B and D

Solution: (a) Events A and B are mutually exclusive because a single die can only land
one way. Obtaining both “one” and “four” at the same time is impossible.
(b) Events B and C are not mutually exclusive because they have the common
outcome “four”. Both events occur if the number “four” is obtained.
(c) Events B and D are mutually exclusive. As shown in the Venn diagram,
there is no overlapping between the two events. It is impossible to get a
number that is both “four” and an odd number in a single toss.

A
B
4 2 1 5
6 3
C D

Example 23

A coin is tossed.
(a) List the possible outcomes.
(b) Define the sample space.
(c) List the simple events.
(d) Are the events mutually exclusive?
(e) Are the events exhaustive?
(f) Assuming that there is equal probability for the coin to land with any of its faces up and that it will
not stand on its edge, find the probability of each event.
Solution: (a) The possible outcomes are head and tail.
Let H represents head and T represents tail.
(b) The sample space, S = {H, T}.
(c) The simple events are {H} and {T}.
Let E = {H} and E = {T}.
2
1
(d) Since on any toss, either H or T may turn up, but not both; the events are
mutually exclusive.

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02 STPM Math(T) T3.indd 88 28/10/2021 10:21 AM