Page 15 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 2 Probability
Definition:
1. The probability that an event will happen is between 0 and 1 inclusive, i.e. 0 < P(E) < 1.

2. P(φ) = 0; φ is 0 collections.
3. P(S) = 1

Example 15

A fair die is tossed. If the event of interest is obtaining a number less than 3, find the probability of the
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event happening.
Solution: There are six different possible outcomes in the sample space for tossing a die,
so S = {1, 2, 3, 4, 5, 6}. Let E be the event of obtaining a number less than 3. 2
Event E has two outcomes satisfying the requirement, we thus have E = {1, 2}.
We use a Venn diagram to show the relationship between S and E.

S
1 2 E

3 4 5 6

The probability of the event E occurring is
P(E) = 2 = 1
6 3
Thus, the probability of getting a number less than 3 is 1 .
3

Definition: If an experiment can result in any one of N different equally likely outcomes, and if exactly n
of these outcomes correspond to event E, then the probability of event E is
P(E) = n
N
Example 16

Two fair coins are tossed.
(a) Use a tree diagram to find the sample space of the above experiment.
(b) List the simple events in the sample space and their corresponding probabilities.
(c) Find the probability of observing exactly one head in the two tosses.
Solution: (a) Let H and T denote head or tail respectively.
The tree diagram is as follows:

First coin Second coin Outcome
H HH
H
T HT
H TH
T
T TT
The sample space of the above experiment is {HH, HT, TH, TT}

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02 STPM Math(T) T3.indd 83 28/10/2021 10:21 AM