Page 37 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 2 Probability
20. A consumer research organisation studies the service under warranty provided by the 200 water purifier
dealers in a city. The information is summarised in the following contingency table:

Good service under Poor service Total
warranty under warranty

Brand A water purifier dealers 65 15 80
Brand B water purifier dealers 45 75 120

Total 110 90 200
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(a) If one of these water purifier dealers is randomly selected, find the probability of choosing a 2
Brand A dealer who provides good service under warranty.
(b) Find the probability that the water purifier dealer provides good service under warranty given
that,
(i) he is from Brand A, (ii) he is from Brand B.

21. There are 48% boys and 52% girls in a classroom. The proportions of wearing spectacles for boys and
girls are shown in the following probability table

Boys Girls Total
Wearing spectacles 0.36 0.42 0.78
Not wearing spectacles 0.12 0.10 0.22
Total 0.48 0.52 1.00

If a student is selected at random from the classroom and is found
(a) to be a boy, find the probability that he wears spectacles.
(b) to be a girl, find the probability that she wears spectacles.
22. Consider the experiment of tossing two coins. The H and T events are defined as follows:
H : Head on the first coin
T : Tail on the second coin
Determine whether the events H and T are independent.

23. In a telephone survey of 900 adults, respondents are asked about the expense of owning a car and
the relative necessity of some form of financial assistance. The respondents are classified according
to whether they currently own a car and whether they think the loan burden for most car owners is
too high, moderate or low. The proportions responding in each category are shown in the following
probability table.
Too high (C) Moderate (D) Low (E)
Owns a car (A) 0.38 0.09 0.01
Does not own a car (B) 0.29 0.13 0.10

If one respondent is randomly chosen, find the probability that the respondent
(a) owns a car,
(b) does not own a car,
(c) owns a car or thinks that the loan burden is too high.
Are the events A and C independent? Explain.

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02 STPM Math(T) T3.indd 105 28/10/2021 10:21 AM