• MCQ Based on the tossing of one coin, two coins and three coins.
• MCQ  Based on the Tossing of one die and two die.
• MCQ Based on the Playing cards
• MCQ Based on the general problems of probability.
• MCQ Based from the CBSE Sample Questions

• In this pdf given below you find the important MCQ which are strictly according to the CBSE syllabus and are very useful for the CBSE Examinations. 
• Solution Hints are also given to some difficult problems. 
• Each MCQ contains four options from which one option is correct.

• First of all students should Learn and write all basic points and Formulas related to the Probability.
• Start solving  the NCERT Problems with examples.
• Solve the important assignments on the Probability.
• Then start solving the following MCQ.

Ans: c

Q 2) What is the probability of a sure event?
a) 0
b) 1
c) 2
d) 3 

Ans: b

Q 3) The probability that cannot exist among the following:
(a) 2 / 3
(b) -1.5
(c) 15%
(d) 0.7 

Ans: b

Q 4) The probability of getting a spade card from a well shuffled deck of 52 cards is
a) 1/ 34
b) 1/ 4
c) 12/ 13
d) 3/ 4 

Ans: b

Q 5) If P(E) = 0.07, then what is the probability of ‘not E’?
(a) 0.93
(b) 0.95
(c) 0.89
(d) 0.90
Ans: a

Explanation: 

P(E) + P(not E) = 1
Since, P(E) = 0.05 

 So, P(not E) = 1 – P(E) 

Or, P(not E) = 1 – 0.07 

 ∴ P(not E) = 0.93

Q 6) The total number of events of throwing 10 coins simultaneously is
(a) 1024
(b) 512

(c) 100
(d) 10
Ans: a Explanation :

 Total events 2¹⁰ = 1024

Q 7) A bag has 3 red balls and 5 green balls. If we take a ball from the bag, then what is the probability of getting red balls only?
(a) 3
(b) 8
(c) 3/8
(d) 8/3 

Ans: c

Q 8) A bag has 5 white marbles, 8 red marbles and 4 purple marbles. If we take a marble randomly, then what is the probability of not getting purple marble?
(a) 0.5
(b) 0.66
(c) 0.08
(d) 0.77 

Ans: d

Q 9) A dice is thrown in the air. The probability of getting odd numbers is
(a) 1/2
(b) 3/2
(c) 3
(d) 4 

Ans: a

Q 10) Three coins are tossed simultaneously. The probability of getting all heads is
a) 1
b) 1/ 2
c) 1/ 4
d) 1/ 8
Ans: d 

Explanation: Here S = [HHH, HHT, HTH, THH, HTT, THT, TTH, TTT] = 8
∴ P(all heads) =1/8

Q 11) If two dice are thrown in the air, the probability of getting sum as 3 will be
(a) 2/18
(b) 3/18
(c) 1/18
(d) 1/36
Ans: c
Explanation: When two dice are thrown in the air:
Total number of outcome = 6 x 6 = 36
Sum 3 is possible if we get (1,2) or (2,1) in the dices. 

Hence, the probability will be = 2/36 = 1/18

Q 12) A card is drawn from the set of 52 cards. Find the probability of getting a queen card.
(a) 1/26
(b) 1/13
(c) 4/53
(d) 4/13 

Ans: b

Q 13) One card is drawn from a well shuffled deck of 52 cards. The probability of getting a king of red color is

a) 1/ 26
b) 1/ 13
c) 1/ 4
d) 1/ 2
Ans: a 

Explanation: Total cards = 52
Total events (S) = 52
a king of red color = 2
P(a king of red color) = 2/52 = 1/26

Q 14) The sum of the probabilities of all the elementary events of an experiment is
(a) 0.5
(b) 1
(c) 2
(d) 1.5 

Ans: b

Q 15) A card is selected at random from a well shuffled deck of 52 playing cards. The probability of its being a face card is
(a) 3/13
(b) 4/13
(c) 6/13
(d) 9/13 

Ans: a

Q 16) One card is drawn from a well shuffled deck of 52 playing cards. The probability of getting a non-face card is
a) 3/ 13
b) 10/ 13
c) 7/ 13
d) 4/ 13
Ans: b 

Explanation: Total cards = 52,
Total face cards = 12
∴ Non-face cards = 52 – 12 = 40
∴ P(a non-face card)= 40/52 = 10/13

Q 17) If an event cannot occur, then its probability is
(a) 1
(b) 3/4
(c) 1/2
(d) 0 

Ans: d

Q 18) If P(A) denotes the probability of an event A, then
(a) P(A) < 0
(b) P(A) > 1
(c) 0 ≤ P(A) ≤ 1
(d) –1 ≤ P(A) ≤ 1 

Ans: c

Q 19)A card is drawn from a deck of 52 cards. The event E is that card is not an ace of hearts. The number of outcomes favorable to E is
(a) 4
(b) 13
(c) 48
(d) 51
Ans: d
Explanation
In a deck of 52 cards, there are 13 cards of heart and 1 is ace of heart.
Given that the event E is that card is not an ace of hearts.

Hence, the number of outcomes favorable to E = 52 – 1 = 51

Q 20) If the probability of an event is p, the probability of its complementary event will be
(a) p – 1
(b) p
(c) 1 – p
(d) 1 – 1/p 

Ans: c

Q 22) In a leap year what is the probability of getting 53 Friday
(a) 1/7
(b) 2/7
(c) 3/7
(d) 5/7 

Ans: b

Q 23) In an ordinary year, what is the probability of getting 52 Tuesday
(a) 1/7
(b) 2/7
(c) 4/7
(d) 6/7
Ans: d
Solution Hint
In an ordinary year probability of getting 53 Tuesday is = 
In an ordinary year probability of not getting 53 Tuesday is = 1-  =  

In an ordinary year probability of getting 52 Tuesday is = 

Q 24) The probability of getting a bad egg in a lot of 400 is 0.035. The number of bad eggs in the lot is
(a) 7
(b) 14
(c) 21
(d) 28
Ans: b
Explanation:
Total number of eggs = 400

Q 25) Two players, Ram and Shyam, play a tennis match. It is known that the probability of Ram winning the match is 0.62. The probability of Shyam winning the match is
(a) 0.62
(b) 0.38
(c) 0.58
(d) 0.42 

Ans: b

Q 26) The probability of getting exactly one head in tossing a pair of coins is
(a) 0
(b) 1
(c) 1/3
(d)1/2
Ans: d
Explanation: Reason: S = [HH, HT, TH, TT] = 4 

Q 27) The letters of the word SOCIETY are placed at random in a row. The probability of getting a vowel is
a) 1/ 7
b) 2/ 7
c) 3/ 7
d) 4/ 7
Ans: c 

Explanation: Total letters = 7
No. of vowel = 3 [∵ Vowel are O, I, E]
∴ P(a vowel) = 3/7

Q 28) Cards bearing numbers 3 to 20 are placed in a bag and mixed thoroughly. A card is taken out from the bag at random. The probability that the number on the card taken out is an even number, is
a) 1/ 20
b) 1/ 4
c) 1/ 3
d) 1/ 2 

Ans: d

Q 29) The total events to throw three dice simultaneously is
(a) 6
(b) 18
(c) 81
(d) 216
Ans: d 

Explanation: 

Total cards = (6)³= 216

Q 30) The probability of getting a consonant from the word MAHIR is
a) 2/ 5
b) 3/ 5
c) 4/5
d) 1 

Ans: b

Q 31) One card is drawn from a well-shuffled deck of 52 cards. The probability that the card will not be an ace is
a) 1/ 13
b) 4/ 13
c) 12/ 13
d) 3/ 13 

Ans: c

Q 32) A girl calculates that the probability of her winning the first prize in a lottery is 8/100 . If 6,000 tickets are sold, how many tickets has she bought?
(a) 400
(b) 750
(c) 480
(d) 240
Ans: c 

Explanation: 

No. of tickets sold = (8/100) × 6000 = 8 × 60 = 480

Q 33)
A man is known to speak truth 3 out of 4 times. He throws a die and a number other than six comes up. Find the probability that he reports it is a six.
a) 3/ 4
b) 1/ 4
c) 1/ 2
d) 1
Ans: b
Explanation:
Probability of telling a truth = 3/4 

Probability of telling a lie = 1- 3/4 = 1/4

When a number other than six appears and man reports it is a six, it means man is telling a lie.
Required Probability = 1/ 4

Q 34) Which of the following cannot be the probability of an event?
(a) 1.5
(b) 3 / 5
(c) 25%
(d) 0.3 

Ans: a

Q 35) An integer is chosen at random from 1 to 100, Find the probability that it is divisible by 4 and 6
a) 4/ 25
b) 8/ 25
c) 7/ 25
d) 2/ 25 

Ans: d

Q 36) An integer is chosen at random from 1 to 100, Find the probability that it is a prime number
a) 4/ 25
b) 8/ 25
c) 1/ 4
d) 2/ 5 

Ans: c

Q 37) A jar contains 24 marbles, some are green and some others are blue. If a marble is drawn at random from the jar, the probability that it is green is 2/ 3. Find the number of blue marbles.
a) 12
b) 10
c) 8
d) 16 

Ans: c

Q 38) Three coins are tossed together. Find the probability of getting at most 2 tails.
a) 7/ 8
b) 3/ 4
c) 1/ 8
d) 5/ 8
Ans: a
Solution Hint
When 3 coins are tossed then possible outcomes are as follows
{HHH, HHT, HTH, THH, HTT, THT, TTH, TTH}
P(Getting at most 2 tail) = P(≤ two tails) = P(2 tail) + P(1 tail) + P(no tail) 

Q 39) A box contains cards numbered 6 to 50. A card is drawn at random from the box. The probability that the drawn card has a number which is a perfect square like 4,9….is

Ans: d

Q 40) If the letters of the word RAMANUJAN are put in a box and one letter is drawn at random. The probability that the letter is A is
(a) 3/5
(b) 1/2
(c) 3/7
(d) 1/3 

Ans: d

Q 41) A fair die is thrown once. The probability of even composite number is
(a) 0
(b) 1/3
c) 3/4
(d) 1 

Ans: b

Q 42) If P (E) denotes the probability of an event E, then 
(a) 0< P(E) ⩽1
(b) 0 < P(E) < 1
c) 0 ≤ P(E) ≤1
(d) 0 ⩽P(E) <1 

Ans: c

Q 43) In a throw of a pair of dice, the probability of the same number on each die is
(a) 1/6
(b) 1/3
c) 1/ 2
(d) 5/6 

Ans: a

Standard Maths SP (041)

Q 44) Two fair coins are tossed. What is the probability of getting at the most one head?
(a) 3 ⁄ 4
(b) 1 ⁄ 4
(c) 1 ⁄ 2
(d) 3 / 8
Ans: a
Solution Hint
Possible outcomes are (HH), (HT), (TH), (TT)
Favorable outcomes(at the most one head) are (HT), (TH), (TT) So probability of getting at the most one head =3/4

Q 45) A letter of English alphabets is chosen at random. What is the probability that it is a letter of the word ‘MATHEMATICS’?
(a) 4/13
(b) 9/26
(c) 5/13
(d) 11/26
Ans: a

Solution Hint
Number of Possible outcomes are 26
Favorable outcomes are M, A, T, H, E, I, C, S probability = 8/26 = 4/13

Q 46) A card is drawn from a well shuffled deck of cards. What is the probability that the card drawn is neither a king nor a queen?
(a) 11/13
(b) 12/13
(c) 11/26
(d) 11/52 

Ans: a

Q 47) Two fair dice are rolled simultaneously. The probability that 5 will come up at least once is
(a) 5/36
(b) 11/36
(c) 12/36
(d) 23/36
Ans: b
Solution Hint
Outcomes when 5 will come up at least once are-
(1,5), (2,5), (3,5), (4,5), (5,5), (6,5), (5,1), (5,2), (5,3), (5,4) and (5,6) Probability that 5 will come up at least once = 11/36

Q 48) Which of the following cannot be the probability of an event.
a) 1/3
b) 0.1
c) 3 %
d) 17/16 

Ans: d

Q 49) If the probability of an event is m. then the probability of its complimentary event is :
a) m – 1
b) m
c) 1 – m
d) 1 + m

Ans: c

Q 50) A dice is thrown once. The probability of getting an even prime number is :
a) 2/3
b) 1/ 2
c) 1/6
d) 0 

Ans: c

Q 51) A letter is drawn at random from the letters of the word MIRROR. Which are the letters that have equal probabilities of being drawn ?
a) I and O
b) M, I, R
c) M, I, O
d) M, I, O, R 

Ans: c

Q 52) In a single through of a pair of dice, the probability of getting the sum a perfect square is :
a)  1/18

b)  7/36
c)  1/36
d)  2/9

Ans: b

Q 53) The probability of getting two heads when two fair coins are tossed together is
a) 1/3
b) 1/4
c) 1/2
d) 1 

Ans: b

Q 54) In a single through of a dice, the probability of getting a composite number is
a) 1/3
b) 1/2
c) 2/3
d) 5/6 

Ans: a

Q 55) The probability that a non-leap year has 53 Wednesday, is:
a) 1/7
b) 2/7
c) 5/7
d) 6/7 

Ans: a

Q 56) From the letters of the word ‘MANGO’ a letter is selected at random. The probability that the letter is a vowel is :
a) 1/5
b) 3/5
c) 2/5
d) 4/5 

Ans: c