Page 35 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 2 Probability
6. A bag contains one blue and two green balls. Two balls are randomly chosen, one at a time. Their
colours are recorded
(a) Use a tree diagram to find the sample space.
(b) Find the probability that both balls are green.

7. Two fair coins are tossed, and the outcome is recorded. The events of interest are listed as
follows:
A : At least one head is observed
B : At least one tail is observed
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C : No head is observed
Define the following events, and find their respective probabilities.
(a) A (b) B 2
(c) C (d) A  B
(e) A  B (f) A

8. A bowl contains three balls, one blue, one green, and one red. A student draws two balls at random,
one at a time with replacement. What is the probability that at least one ball is red?

9. A box contains six balls, two blue and four green. Two balls are drawn at random in succession without
replacement. Find the probability that exactly one is green.

10. An experiment consists of casting a die and recording whether the number of up face is even or odd.
If the number is odd, then a coin is tossed once and the up face is recorded. If the number is even,
then the coin is tossed twice and the up face is recorded for each toss. Use a tree diagram to determine
the sample space of the experiment and find the probability that,
(a) at least one head appears,
(b) no heads appear, and
(c) no tails appear.
What is the relation between the events for parts (a) and (b)?

11. An ordinary deck of cards contains 52 cards divided into four suits:
The red suits are diamonds (◆) and hearts (♥) and
the black suits are clubs (♣) and spades (♠).
Each suit contains 13 cards of the following denominations:
2, 3, 4, 5, 6, 7, 8, 9, 10, J(jack), Q(queen), K(king), and A(ace).
The cards J, Q, K, and A are called face cards.
(a) List the sample space of the outcomes.
(b) State the event that the chosen card is a red face card.
(c) Find the probability that the chosen card is a red face card.

12. A die is one of a pair of dice. It is a cube with six sides, each containing from one to six dots,
called pips. Suppose a black die and a green die are tossed together, and the numbers of dots that
occur face up on each are recorded.
(a) Give a collectively exhaustive list of the possible outcomes.
(b) Use set notation to write the event E that the numbers showing face up have a sum of 7.
(c) Find the probability that the numbers showing face up have a sum of 7.

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02 STPM Math(T) T3.indd 103 28/10/2021 10:21 AM