FAD1015: Mathematics III — Tutorial 3

Centre for Foundation Studies in Science
Universiti Malaya
Session 2025/2026

Topic: Probability, Mutually Exclusive

Question 1

A number is randomly selected from the set {1, 2, 3, …, 250}. What is the probability that it is:

(a) divisible by 5,

(b) odd,

Question 2

A card is dealt from a well shuffled ordinary pack of 52 playing cards.

(a) Find the probability that the card dealt is:

i. a Queen,

ii. a heart or diamond,

iii. a picture card showing spades.

(b) Two cards are dealt and put face-up on the table. They are the 4 of clubs and the 7 of diamonds. A third card is now dealt. What is the probability that it is a club or 7?

Question 3

The table show the distribution of grades in the Mathematics paper in semester 1.

	A	B	C	Fail
Physical Science	0.069	0.135	0.09	0.006
Biological Science	0.141	0.205	0.10	0.024
APIDS	0.063	0.135	0.025	0.007

Find the probability that a randomly chosen student is:

(a) from physical science,

(b) gets an A,

(d) gets a B and from APIDS,

(e) Physical science or gets at least a B,

(f) neither APIDS nor fail.

Question 4

Hariz is given a bag of 20 sweets of which 6 are strawberry flavoured, 6 are lemon flavoured and 8 are orange flavoured. He takes out 5 sweets at random and eats them. Find the probability that he eats:

(a) 5 orange flavoured sweets,

(b) 3 strawberry flavoured and 2 lemon flavoured sweets,

(d) no lemon flavoured sweets.

Question 5

The probability of the events A, B and C is given below.

$P(A) = 0.40$, $P(B) = 0.37$, $P(A \cup B) = 0.55$, $P(A \cap C) = 0.10$, $P(C) = 0.31$ and B and C are mutually exclusive.

Using the Venn Diagram, evaluate:

(a) $P(A \cap B)$

(b) $P(A \cup C)$

(d) $P(B' \cap C)$

(e) $P(A \cup B \cup C)'$

Question 6

The probability that a randomly chosen boy in Class B2 is in the basketball team is 0.4, the probability that he is in the hockey team is 0.5 and the probability that he is in both teams is 0.2.

Find the probability that a boy chosen at random from the class:

(a) is in the basketball team, but not in the hockey team,

(b) is in the basketball team or the hockey team,

Question 7

From an ordinary pack of 52 playing cards, the 7 of diamonds has been lost. A card is dealt from the well-shuffled pack. Find the probability that the card is:

(a) a diamond,

(b) a Queen,

(d) a diamond or a seven.

Question 8

Two fair coins are tossed.

(a) Events A and B are mutually exclusive. A is the event 'at least one head is obtained'. Define event B.

(b) X is the event 'one head is obtained'. Define an event Y such that X and Y are not mutually exclusive.

Related Concepts

Probability — measure of likelihood of an event
Mutually Exclusive Events — events that cannot occur together
Venn Diagram — visual representation of set relationships
Sample Space — set of all possible outcomes
Conditional Probability — probability given certain conditions

Source: FAD1015 Questions T1-T6 _20252026.pdf