Page 29 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 2 Probability
If events A and B are independent, then P(A | B) = P(A).

Hence, P(A  B) = P(A) × P(B)

This is the multiplication rule for independent events.
In words, two events are independent if and only if the probability that both events will happen is found
by multiplying their individual probabilities.
The above relationship is the multiplication law of probability for independent events. It provides a simple
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way to check whether events are independent.

Example 32 2

A couple has five children. Assume that the probability of getting a boy or a girl is 1 . Find the probability
that 2
(a) all five are boys, (b) three are girls and two are boys.

Solution: Let event A = a child is a boy,
event B = the couple has three girls and two boys.

(a) Knowing that the child is a boy has no influence on the next birth, so the
five births are independent of one another.
Given P(A) = 1 ,
2
we have P(all five children are boys) = 1 × 1 × 1 × 1 × 1
2 2 2 2 2
= 1
32
Hence, the probability that all five are boys is 1 .
32
(b) One of the possible birth orders to get three girls and two boys is GGGBB.
The probability of this combination is

= 1 × 1 × 1 × 1 × 1
2 2 2 2 2
= 1
32
The number of possible combinations to position three girls in the birth
5
order of five children is C
3
= 5 × 4 × 3
3 × 2 × 1
= 10
Each combination would have the same probability of 1 .
32
Thus, P(B) = 10 × 1
32
= 5
16
Hence, the probability of getting three girls and two boys is 5 .
16

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02 STPM Math(T) T3.indd 97 28/10/2021 10:21 AM