Page 17 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 2 Probability
In summary, if the number of equally probable outcomes in the sample space S is denoted by n(S) and the
number of equally probable outcomes in an event E is written as n(E), then the probability of an event to
occur can be expressed as P(E) = n(E) .
n(S)

As E is a subset of S, we have 0 < n(E) < n(S).

Dividing all by n(S), 0 < n(E) < n(S)
n(S) n(S) n(S)
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Thus, we get 0 < P(E) < 1.
2
Another approach in determining the probability is based on relative frequency. If an experiment is repeated
n times under the identical condition and an event is observed to happen f times, the probability of the
event happening is then estimated to be

P(E) = frequency of the event occured = f
total number of observations n

Example 18

Data are collected on the gender of customers who enter a supermarket on a particular day. It is found
that out of 360 customers, 249 are females. Find the probability that a customer who visits the supermarket
on that day is a female customer.
Solution: Let A be the event that a female customer visits the supermarket.

P(A) = 249 = 83
360 120

Complementary
Events
Complementary events INFO
Two events are said to be complementary, if one event happens then the other event cannot happen at the
same time. Both events contain all the experimental outcomes in the sample space. Let E (read as E prime)
denotes the event E does not happen where E is called the complement of E. If n(S) is the size of the sample
space, n(E) is the number of outcomes in event E, then n(E) = n(S) – n(E). Hence, in terms of probability

P(E) + P(E) = n(E) + n(E) = n(E) + n(S) – n(E) = n(S) = 1
n(S) n(S) n(S) n(S)

This rule for complementary events states that if two events are complementary, then the sum of their
probabilities equal to 1. Hence,
P(event E happens) + P(event E does not happen) = 1.
Rearranging this equation we obtain the complement rule as follows:

P(E) = 1 – P(E)

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02 STPM Math(T) T3.indd 85 28/10/2021 10:21 AM