Page 34 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 2 Probability

We are interested in finding P(S | D), the probability of a unit from supplier 3
3
given that the unit is defective.
From the tree diagram, the probability of selecting a defective unit is

P(D) = 0.6 × 0.02 + 0.24 × 0.03 + 0.16 × 0.05
= 0.0272

and the probability that the selected unit is from supplier 3 and is defective is
P(S  D) = 0.16 × 0.05
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3
= 0.008
2 P(S | D) = product of branch probabilities leading to D through S 3
3 sum of all branch probability products leading to D

= 0.16 × 0.05
0.6 × 0.02 + 0.24 × 0.03 + 0.16 × 0.05
= 0.008
0.0272
= 0.2941
The probability of a unit from supplier 3 given that the unit is defective is 0.2941.

Exercise 2.2

1. Consider the experiment about a team’s result in a football match.
(a) Determine the sample space.
(b) Write the following events.
(i) The team wins the match
(ii) The team does not lose the match
2. A number is randomly picked from a set of integers, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}.
(a) Find the sample space of the above experiment.
(b) List the outcomes in the following events for the above experiment.
(i) The number is divisible by 4.
(ii) The number is an odd number.
(iii) The number is 12.

3. An experiment involves flipping a fair coin twice and recording the resulting sequence of happenings.
(a) Describe the sample space of this experiment.
(a) Determine the event that at least one tail appears.
4. A fair die is thrown once. If the event of interest is obtaining a number less than 3, find the probability
of the event happening.
5. A jar contains 2 red marbles, 4 yellow marbles and 3 green marbles. A marble is drawn at random.
(a) Describe the sample space S of this experiment.
(b) Find the probability that
(i) the marble is yellow,
(ii) the marble is not green.

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02 STPM Math(T) T3.indd 102 28/10/2021 10:21 AM