Page 38 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 2 Probability
24. Consider the experiment of tossing a fair dice. The events E and F are defined as follows:
E : Observe an even number
F : Observe a number less than or equal to 4 is obtained
Determine whether the events E and F are independent.
25. The probability that John will like a new sport is 0.70 and the probability that Peter, his brother, will
like it is 0.60. If the probability is 0.28 that he will like it and Peter will dislike it, what is the probability
that he will like it given that Peter is not going to like it?
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26. Two thousand randomly selected adults are asked whether or not they have never shopped on the
internet. The following table gives a two-way classification of the responses obtained.
2
Have shopped (H) Have never shopped (N)
Male (M) 554 386
Female (F) 612 448

Suppose one adult is selected at random from these 2000 adults. Find the probability that
(a) the adult has never shopped on the internet.
(b) the adult has shopped on the Internet or is a female.
(c) the adult is a male given that the adult has shopped on the internet.

27. A production process uses two machines in its daily production. A random sample of 500 items
produced are inspected and the following contingency table is obtained.

Defective Non-defective
Machine X 15 285

Machine Y 6 194

If an item is selected randomly, what is the probability that the item is
(a) defective,
(b) produced by machine Y and defective,
(c) produced by machine X or non-defective,
(d) defective given that it is produced by machine X.

28. Suppose there are two containers C and C . C has eight blue balls and two red balls, while C has four
2
2
1
1
blue balls and six red balls. If a container is selected randomly, and a ball is then selected randomly
from that container, the sequential process and probabilities is shown by the following tree diagram.
B
0.8
C 1
0.5
0.2
R
B
0.4
0.5
C
2
0.6
R
Find the probability that a selected red ball come from C .
1

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02 STPM Math(T) T3.indd 106 28/10/2021 10:21 AM