Page 14 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 2 Probability

Example 14

A number is randomly picked from a set of integers, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
(a) Find the sample space of the above experiment.
(b) List the outcomes in the following events for the above experiment.
(i) The number is divisible by 3.
(ii) The number is an even number.
(iii) The number is 11.
Note: By picking an integer at random, we mean that each integers has equally likely chance of
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being picked.
2 Solution: (a) There are ten possible outcomes, so the sample space is S = {1, 2, 3, 4, 5,
6, 7, 8, 9, 10}.
(b) (i) The event of the number divisible by 3 has three possible outcomes,
3, 6 or 9.
E = {3, 6, 9}
(ii) The event of obtaining an even number has five possible outcomes,
2, 4, 6, 8, 10.
E = {2, 4, 6, 8, 10}
(iii) The set has ten integers and none of these integers is 11. So,
picking a number 11 is impossible. We say it is an impossible event
and E = {φ}

Probability of an event
If you are planning to visit your friend who is staying nearby, then you look at the sky and you are not sure
whether it is going to rain. So, you are hesitating to bring along an umbrella with you. This is one of the
non-deterministic situations that we encounter often. In the real world, many problems cannot be predicted
with accuracy. Probabilities are thus introduced to deal with situations involving randomness or uncertainty
about the outcome.
Probability is a measure of how likely an event is to happen. In an experiment, if all the outcomes are
equally likely to occur, then the probability of an event to occur is the number of ways that an event can
occur divided by the total number of outcomes in the sample space.
number of ways that an event can occur
P(Event) =
total number of possible outcomes

The probability of an event is a number between 0 and 1 that indicates the likelihood the event will occur
as shown below:

P(E) = 0 P(E) = 0.5 P(E) = 1

Note: 1. P(E) = 0 means that the event will not occur.
2. P(E) = 1 means that the event is certain to occur.
3. P(E) = 0.5 means that the event is equally likely to occur or not occur.
4. The closer the probability of a given event is to 1, the more likely it is to occur.
5. Probability can be expressed as decimal, fraction, ratio or percentage.
6. For example: P(E) = 0.5, 1 or 50%.
2

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02 STPM Math(T) T3.indd 82 28/10/2021 10:21 AM