Page 44 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 2 Probability
30. A production process uses two machines in its daily production. A random sample of 500 items
produced were inspected and listed in the table below.

Defective Non-defective

Machine A 15 285
Machine B 6 194
If an item is selected randomly,
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(a) find the probability that the item is
(i) defective,
2 (ii) produced by Machine A or non-defective,
(iii) defective given that it is produced by Machine A,
(b) determine whether
(i) the events “Machine A” and “defective” are independent,
(ii) the events “Machine B” and “non-defective” are mutually exclusive.

31. In a school, 45% of the students are males and 25% of the students play badminton. 11.25% of the
students are male students who play badminton. Events A and B are defined as follows:
A : A male student of the school is selected.
B : A student of the school, who play badminton, is selected.
(a) Find P(A), P(B), and P(A  B).
(b) Determine whether
(i) A and B are mutually exclusive,
(ii) A and B are independent.
(c) Find P(A | B). What can you conclude?

32. Of the applications to a certain course, 70% are eligible to enter and 30% are not. To aid in the selection
process, an admissions test is conducted that is designed so that an eligible candidate will pass 80%
of the time, while an ineligible student will pass only 20% of the time.
(a) Find the probability that a student will pass the admissions test.
(b) If a student passes the admissions test, what is the probability that the student is eligible?

33. A bag contains 10 table tennis balls, of which 4 are dented. All table tennis balls look alike and have
equal probability of being chosen. Three table tennis balls are selected and placed in a bag. Find the
probability that
(a) all 3 are dented,
(b) exactly 2 are dented,
(c) at least 2 are dented.

34. A pharmaceutical company had developed a new diabetes treatment which is being tested on 1000
volunteers. In the test, 600 volunteers received the treatment and some a placebo (a harmless neutral
substance). It is found that 250 showed some improvement. It is also found that 450 received treatments
showed no improvement.
(a) Construct a two way classification table based on the above information.
(b) Find the probability that a random chosen volunteer
(i) showed some improvement after receiving a placebo,
(ii) received treatment or showed no improvement.
(c) Determine whether the events “a volunteer received treatment” and “a volunteer showed some
improvement” are independent. Explain.

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02 STPM Math(T) T3.indd 112 28/10/2021 10:21 AM