Page 24 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 2 Probability

Using the formula, P(A  B) = P(A) + P(B) – P(A  B), we get

P(A  B) = 91 + 37 – 16
150 150 150

= 56
75
The probability that the selected student reads newspaper or a magazine is 56 .
75
Penerbitan Pelangi Sdn Bhd. All Rights Reserved.

2 Conditional probability
A box contains 6 red and 4 green balls. Suppose two balls are chosen at random from this box. Let us
define two events, A = the first ball is red and B = the second ball is red. Consider the situation that the
ball is chosen without replacement. The calculation of the probability that the first ball chosen is red P(A)
is straight forward and it is found to be 6 = 3 . What about the probability of choosing the second red
10 5
ball P(B)? To compute P(B) we need to know whether the event that the first ball drawn is red or did not
happen. This example introduces an important concept called conditional probability.
In many circumstances the probability of an event is affected by the occurrence of another event. Conditional
probability is defined as the probability of event A happening given that event B has happened. It is denoted
by P(A | B).
Note: Conditional events:
If A and B are two events such that A will occur given that B has already occurred, then A given
B or A | B is the event A conditional on B happening.
The vertical bar “ | ” is read as “given that”.

Consider the following Venn diagram. Suppose that event B is chosen and we wish to find the probability
that event A is being picked. Now the sample space is reduced from the original sample space S to B with
this additional information.
S
A B

Thus, to compute the conditional probability of the event A given that event B occurred, denoted by P(A |
B), we need to count the numbers of elements in event A  B as well as in event B.

We could write P(A | B) = n(A  B) . Divide both numerator and denominator by the total number of
n(B)
elements in the sample space n(S) to get
n(A  B)
P(A | B) = n(S)
n(B)
n(S)
= P(A  B) .
P(B)

92

02 STPM Math(T) T3.indd 92 28/10/2021 10:21 AM