Page 36 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 2 Probability
13. When drawing a card from a deck of playing cards, determine whether the following events are
mutually exclusive:
(a) the events “ace” and “king”,
(b) the events “ace” and “spade”.
Hence, find in a single draw, the probability of drawing,
(c) either an “ace” or a “king”,
(d) an “ace” or “spade” or both.

14. A die is cast.
(a) List the possible outcomes.
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(b) List the simple events.
(c) Define the sample space.
2 (d) Are the events mutually exclusive?
(e) Are the events exhaustive?
(f) Assuming that there is equal probability for the die to land with any of its faces up and that it
will not stand on its edge, find the probability of each event.

15. Consider the experiment of casting two fair dice, one black and one white and the separate numbers
shown uppermost are observed. List the outcomes as ordered pairs, (b, w) on a table where b and w
represent the numbers shown uppermost on black and white respectively.
Events E , E and E are defined as follows:
2
3
1
E = The number shown uppermost on the black dice exceeds that on the white dice.
1
E = The number shown uppermost on the black dice exceeds 2.
2
E = The total number shown uppermost on both dice is less than 9.
3
(a) Verify that P(E ) + P(E ) = P(E  E ) + P(E  E )
1 2 1 2 1 2
and P(E ) + P(E ) = P(E  E ) + P(E  E )
1 3 1 3 1 3
(b) Identify a pair of events that are exhaustive.
(c) What is the relation between E ' and E '.
2
3
(d) Find P(E  E ) and P(E '  E ').
2
3
3
2
16. It is given that, for events A and B,
P(A) = 0.5, P(A  B) = 0.9 and P(A  B) = 0.2. Find
(a) P(B) (b) P(A  B' )
(c) P(A'  B) (d) P(A'  B' )
17. In a swimming competition in which there are no dead heats, the probability that swimmer A wins is
0.4, the probability that swimmer B wins is 0.3 and the probability that swimmer C wins is 0.2. Find
the probability that
(a) swimmer A or B wins,
(b) swimmer A or B or C wins,
(c) someone else wins.
18. Events C and D are mutually exclusive such that, P(C) = 2 and P(D) = 3 . Find
5 10
(a) P(C) (b) P(D) (c) P(C  D)
(d) P(C  D) (e) P(C  D) (f) P(C  D)

19. The probabilities that it will rain in a town on a day in mid-September, that there will be a thunderstorm
on that day, and that there will be rain as well as a thunderstorm are 0.28, 0.23 and 0.16 respectively.
What is the probability that there will be rain and/or a thunderstorm in the town on such a day?

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02 STPM Math(T) T3.indd 104 28/10/2021 10:21 AM