Page 33 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 2 Probability

Example 36

A telemarketing company makes a total of 100 phone calls to its customers, 60 calls in the morning and
40 calls in the afternoon. The successful rates of selling its products in the morning and in the afternoon
are 0.25 and 0.16 respectively. Find the total successful rate of the company in selling its products.
Solution: Let A represents a morning call,
1
A represents an afternoon call,
2
B represents a sale of a product,
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Events A and A are mutually exclusive.
1 2
40
60
P(A ) = 100 P(A ) = 100
2
1
= 0.6, = 0.4, 2
P(B | A ) = 0.25 and P(B | A ) = 0.16
1
2
By the rule of total probabilities, we have
P(B) = P(A ) × P(B | A ) + P(A ) × P(B | A )
2
1
2
1
= 0.6 × 0.25 + 0.4 × 0.16
= 0.214
Hence, the total successful rate of the company in selling its products is 0.214.
Example 37
A shop ordered certain item from three different suppliers. The table below shows the distribution of the
current stock of the item and the corresponding percentages of defective units.
Supplier 1 Supplier 2 Supplier 3
Stock 150 60 40
Defective units 2% 3% 5%

If a unit is selected at random from the item stock and is found to be defective, find the probability that
the selected unit came from supplier 3.

Solution: We form a tree diagram and place appropriate probability on each branch as
shown.
Let S , S and S represent the events that the item unit are from suppliers 1, 2
3
2
1
and 3 respectively and D be the event that the selected unit is defective.

Supplier Defective or good
defective
0.02
1
0.98 good
0.6
0.03 defective
0.24
2
0.97 good
0.16 defective
0.05
3
0.95 good

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02 STPM Math(T) T3.indd 101 28/10/2021 10:21 AM