Page 30 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 2 Probability

Example 33

Two events C and D are such that P(C) = 2 and P(D) = 1 . If
5 3
(a) P(C  D) = 11 , (b) P(C  D) = 9 ,
15 15
determine if C and D are mutually exclusive and find also if C and D are independent.

Solution: (a) By using P(C  D) = P(C) + P(D) – P(C  D)
11 = 2 + 1 – P(C  D)
15 5 3
2 P(C  D) = 0
\ C and D are mutually exclusive.
P(C) × P(D) = 2 × 1 = 2
5 3 15
Since P(C  D) ≠ P(C) × P(D), C and D are not independent.

(b) By using P(C  D) = P(C) + P(D) – P(C  D)
9 = 2 + 1 – P(C  D)
15 5 3
P(C  D) = 2
15
Since P(C  D) ≠ 0, C and D are not mutually exclusive.

As P(C  D) = P(C) × P(D), C and D are independent.
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Example 34

The probability that a new released model of printer will develop a fault within a year is 0.2. If two new
printers are selected at random from a store, determine the probability that only one printer will develop
a fault.
Solution: We start with a tree diagram showing all the possible combined outcomes of the
two experiments, the happening of the first and second printers.
The first set of branches of the tree shows what could happen to the first printer
and the second set of branches indicates what could happen to the second printer.
Since a printer has two possible outcomes, fault or no fault and each of these
may lead to two other possible outcomes of the second printer, we have a total
of 2 × 2 = 4 possible outcomes.
First printer Second printer
fault
0.2
fault
0.2
0.8 no fault
0.2 fault
0.8
no fault
0.8
no fault

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02 STPM Math(T) T3.indd 98 28/10/2021 10:21 AM