1
A fair coin is tossed once. What is the probability of getting a head?
Correct answer: C. 1/2
There are two equally likely outcomes (head, tail), and one is a head: 1/2.
easy
Sets and Probability MCQs
Solved mathematics MCQs on basic probability with coins, dice, cards and bags, and on sets, unions, intersections and Venn diagram counting, for PPSC, FPSC and NTS tests.
20 MCQsUpdated 30 October 2026
These MCQs introduce probability with coins, dice, cards and bags of balls, and cover sets: unions, intersections, differences, subsets and Venn diagram problems such as how many students like neither of two subjects.
Probability is favourable outcomes divided by total outcomes, so list the outcomes carefully. For Venn problems use n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Every answer here was calculated and checked by script.
- 2
A fair die is rolled. What is the probability of getting a number greater than 4?
Correct answer: B. 1/3
Only 5 and 6 are greater than 4: 2 favourable outcomes out of 6 = 1/3.
easy - 3
A fair die is rolled. What is the probability of getting a prime number?
Correct answer: B. 1/2
The primes on a die are 2, 3 and 5: 3 out of 6 = 1/2. (1 is not prime.)
medium - 4
Two fair coins are tossed together. What is the probability that both show heads?
Correct answer: A. 1/4
The outcomes are HH, HT, TH and TT; only HH works: 1/4.
easy - 5
A card is drawn from a well-shuffled pack of 52 cards. What is the probability that it is an ace?
Correct answer: B. 1/13
There are 4 aces among 52 cards: 4/52 = 1/13.
easy - 6
A card is drawn from a pack of 52 cards. What is the probability that it is the king of hearts?
Correct answer: A. 1/52
There is exactly one king of hearts in 52 cards.
easy - 7
A bag has 3 red and 5 blue balls. One ball is drawn at random. What is the probability that it is blue?
Correct answer: B. 5/8
5 of the 8 balls are blue: 5/8.
easy - 8
Two dice are thrown together. What is the probability that the sum is 7?
Correct answer: C. 1/6
Six of the 36 outcomes give 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). 6/36 = 1/6.
medium - 9
Two dice are thrown together. What is the probability that the sum is 12?
Correct answer: A. 1/36
Only (6, 6) gives 12: 1 out of 36.
medium - 10
The probability of an impossible event is:
Correct answer: A. 0
Probabilities lie between 0 (impossible) and 1 (certain).
easy - 11
If the probability that it will rain tomorrow is 0.3, what is the probability that it will not rain?
Correct answer: C. 0.7
P(not A) = 1 − P(A) = 1 − 0.3 = 0.7.
easy - 12
If A = {1, 2, 3, 4} and B = {3, 4, 5}, what is A ∩ B?
Correct answer: A. {3, 4}
The intersection contains the elements common to both sets: 3 and 4.
easy - 13
If A = {1, 2, 3, 4} and B = {3, 4, 5}, how many elements does A ∪ B have?
Correct answer: B. 5
A ∪ B = {1, 2, 3, 4, 5}; common elements are counted only once.
easy - 14
If n(A) = 20, n(B) = 15 and n(A ∩ B) = 5, what is n(A ∪ B)?
Correct answer: B. 30
n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 20 + 15 − 5 = 30.
medium - 15
In a class of 40 students, 25 like tea, 20 like coffee and 10 like both. How many like neither?
Correct answer: B. 5
Students who like at least one = 25 + 20 − 10 = 35, so 40 − 35 = 5 like neither.
medium - 16
How many subsets does a set with 3 elements have?
Correct answer: C. 8
A set with n elements has 2ⁿ subsets: 2³ = 8 (including the empty set and the set itself).
medium - 17
If A = {1, 2, 3, 4, 5} and B = {4, 5, 6}, what is A − B?
Correct answer: B. {1, 2, 3}
A − B contains the elements of A that are not in B: 1, 2 and 3.
medium - 18
In a group of 40 boys, each plays cricket or hockey or both. If 30 play cricket and 20 play hockey, how many play both?
Correct answer: B. 10
Both = 30 + 20 − 40 = 10, because everyone plays at least one game.
medium - 19
A letter is chosen at random from the word PAKISTAN. What is the probability that it is a vowel?
Correct answer: C. 3/8
PAKISTAN has 8 letters, and 3 are vowels (A, I, A): 3/8.
medium - 20
What is the probability that a leap year, chosen at random, has 53 Sundays?
Correct answer: A. 2/7
A leap year has 52 full weeks plus 2 extra days. Of the 7 possible pairs of extra days, 2 include a Sunday (Sat–Sun, Sun–Mon): 2/7.
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