Chapter 15: Probability – Chapter-Wise Important Questions and Answers | Class 10 Mathematics CBSE Solutions
CBSE Class 10 Mathematics Chapter 15: Probability Important Questions with Solutions and Answers
Chapter 15: PROBABILITY
SECTION = A
Question: The probability that a 2-digit number less than 20, selected at random will be a multiple of 2 and not a multiple of 3, is [2025 Standard]
(a) 
(b) 
(c) 
(d) 
Solution: (c)
[ Total number of possible outcomes 
[10, 11 , …..19]
The favourable number of elementary events = 3 [10 , 14 , 16 ]
]
Question: Cards numbered 10, 11, 12, ..., 30 are kept in a box and shuffled thoroughly. Rohit draws a card at random from the box. The probability that the number on the card is a multiple of 4 or 5 is : [2025 Standard C]
(a) 
(b) 
(c) 
(d) 
Solution: (b)
[ Total number of possible outcomes 
So, the number of favorable outcomes 
]
Question: The probability of getting a sum of 8, when two dice are thrown simultaneously, is : [2024 Standard]
(a) 
(b) 
(c) 
(d) 
Solution : (d)
[ Total number of possible outcomes 
So, the number of favorable outcomes = 5 [(2,6),(3,5),(4,4) , (6,2) ,(5,3)]
]
Question: When a die is thrown, the probability of getting an odd number greater than 3 is : [2024 Basic]
(a) 
(b) 
(c) 
(d) 0
Solution: (a)
[ Total possible outcomes = 6
So, the number of favorable outcomes = 1 [only 5]
]
Question: Two dice are rolled together . The probability of getting a doublet is : [2024 Basic]
(a) 
(b) 
(c) 
(d) 
Solution: 
(c)
[ Total possible outcomes = 6 × 6 = 36
So, the number of favorable outcomes = 6 [(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)]
]
Question: A girl calculates that the probability of her winning the first prize in a lottery is 0.08. If 6000 tickets are sold, how many tickets has she bought ?
(a) 40 (b) 240 (c) 480 (d) 750
Solution: (c) 480
[ Given, Probability = 0.08 , Total tickets = 6000
Let, x be the number of tickets she bought .
A/Q, 
]
Question: Probability of happening of an event is denoted by p and probability of non-happening of the event is denoted by q .Relation between p and q is : [2023 Standard]
(a) 
(b) 
(c) 
(d) 
Solution: (a)
[An event either happens or does not happen, so their probabilities must add up to the total certainty of 1.]
Question: A die is rolled once. The probability that a composite number comes up, is : [2023 Basic]
(a) (b) 
(c) 
(d) 0
Solution: (c)
[ Total number of possible outcomes = 6
So, the number of favorable outcomes = 2 [4 , 6 ]
]
Quesion: A die is thrown once. Find the probability of getting a number less than 7. [2023 Basic]
(a) 
(b) 1 (c) 
(d) 0
Solution: (b) 1
[ Total number of possible outcomes = 6
So, the number of favorable outcomes = 6 [ 1,2,3,4,5,6]
]
Question: A card is drawn at random from a well-shuffled deck of 52 cards. The probability of getting a red card is : [2023 Basics]
(a) 
(b) 
(c) 
(d) 
Solution: (d)
[ Total number of possible outcomes = 52
The number of outcomes favourable = 13 + 13 = 26
]
Question: If two different dice are rolled together, the probability of getting an even number on both dice is : [2014 Dehli ]
(a) 
(b) 
(c) 
(d) 
Solution : (d) [ P(getting an even number on both dice) 
]
Question: Which one of the following is the probability of an event ? [SEBA 2017]
(a) 
(b) 
(c) – 1.5 (d) 1.001
Solution : (a) [ The probability of an even E is a number P(E) such that 
]
Question: Two different coins are tossed simultaneously . The probability of getting at least one head is : [CBSE 2014F]
(a) (b) 
(c) 
(d) 
Solution : (c) [ P(getting at least one head) 
{ HH , HT , TH } ]
Question: A bag contain 8 red , 6 white and 4 black balls . A ball is drawn at random from the bag. Then the probability that the drawn ball getting neither white nor black is :
(a) 
(b) 
(c) 
(d) 
Solution : (b) [ P(getting neither white nor black) 
]
Question: The sum of the probabilities of all the elementary events of an experiment is : [SEBA 2020]
(a) 1 (b) 1.25 (c) 1.4 (d) 2
Solution : (a) 1 [ The sum of the probabilities of all the elementary events of an experiment is 1 .]
Question: The probability that a number selected at random from the numbers 1 , 2 , 3 , ……, 15 is a multiple of 4 is : [2014]
(a) 
(b) 
(c) 
(d) 
Solution : (d) [ P(getting a multiple of 4) 
{4 , 8 , 12} ]
Question: A number is selected from the first 100 natural numbers . The probability that the number is divisible by 7 is : [SEBA 2016]
(a) 
(b) 
(c) 
(d) 
Solution : (a) [ P(getting a number divisible by 7) 
{7,14,21,28,35,42,49,56,63,70,77,84,91,98} ]
Question: If for any event 
, 
, when 
means ‘‘ an event not happen E ’’ then the value
is : [SEBA 2014]
(a) 1.00 (b) 9.99 (c) 0.89 (d) 1.11
Solution: (c) 0.89 [ We have , 
]
Question: Which of the following cannot be the probability of an event ?
(a) (b) 
(c) 15 % 
(d) 0.7
Solution: (b)
Question: In a family of 3 children, the probability of having at least one boy is : [ CBSE 2014]
(a) 
(b) 
(c) 
(d) 
Solution : (d)
[ Total number of possible outcome 
The number of at least one boy 
]
Question: 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
Solution: (c) 0 ≤ P(A) ≤ 1 .
Question: If the probability of an event is 
, the probability of its complementary event will be
(a) 
(b) (c) 
(d) 
Solution: (c) .
Question: Which of the following cannot be the probability of an event?
(a) 
(b) 0.1 (c) 3% (d) 
Solution: (d)
[ Here, 
]
Question: A bag contains 3 red balls, 5 white balls and 7 black balls. What is the probability that a ball drawn from the bag at random will be neither red nor black?
(a) 
(b) 
(c) 
(d) 
Solution: (b)
[ Total number of balls = 3 + 5 +7 = 15
]
Question: If an event cannot occur, then its probability is
(a) 1 (b) 
(c) 
(d) 0
Solution: (d) 0
Question: Which of the following can be the probability of an event?
(a) – 0.04 (b) 1.004 (c) 
(d) 
Solution: (c)
[ Since , 
. So, 
]
Question: 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) 
(b) 
(c) 
(d)
Solution: (a)
[ The number of face cards = 12
]
Question: When a die is thrown, the probability of getting an odd number less than 3 is
(a) 
(b) (c) 
(d) 0
Solution: (a) .
[ Total number of outcome = 6
P(getting an odd number less than 3)
]
Question: 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 favourable to E is
(a) 4 (b) 13 (c) 48 (d) 51
Solution: (d) 51 .
[ Total cards in a deck = 52
So, number of unfavorable outcomes = 1
Favorable outcomes=Total outcomes − Unfavorable outcomes = 52 – 1 = 51 ]
Question: 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
Solution: (B) 14
[ Number of bad eggs = 400 ×0.035 = 14
So, the number of bad eggs in the lot is 14. ]
Question: A girl calculates that the probability of her winning the first prize in a lottery is 0.08. If 6000 tickets are sold, how many tickets has she bought?
(a) 40 (b) 240 (c) 480 (d) 750
Solution: (c) 480
[ Probability of winning the first prize = 0.08
Total tickets sold = 6000
Let, x be the number of tickets she bought .
A/Q, 
]
Question: One ticket is drawn at random from a bag containing tickets numbered 1 to 40. The probability that the selected ticket has a number which is a multiple of 5 is
(a) 
(b) 
(c) 
(d) 
Solution: (a)
[ Total number of tickets = 40
The number is a multiple of 5 = 8 [5, 10 ,15 , 20 ,25 , 30 , 35 , 40]
]
Question: Someone is asked to take a number from 1 to 100. The probability that it is a prime is
(a) 
(b) 
(c) 
(c) 
Solution: (c)
Total number from 1 to 100 = 100
The number of a prime number from 1 to 100 = 25
]
Filled in the blanks
Question: Probability of an event 
+ Probability of the event ‘ not ’ 
.
Solution : 1 [ Since, 
]
Question: A die is thrown once , then the probability of getting a number greater than 4 is 
.
Solution : 
[ P(getting a number greater than 4) 
{5 , 6} ]
Question: The probability of an event 
is a number 
such that 
.
Solution : 
.
Question: One card is drawn from a well-shuffled deck of 52 cards , then the probability of getting a spade is 
. [SEBA 2018]
Solution : 
[ P(getting a spade) 
]
Question: The probability that it will rain tomorrow is 0.85 , then the probability that it will not rain tomorrow is .
Solution : 0.15 [ We have , 
]
Question: The sum of the probabilities of all the elementary events of an experiment is 
.
Solution : 1
Question: The probability of an event that is certain to happen is 0 . Such an event is called 
.
Solution : impossible event .
Question: For any event , 
, Where
stands for ‘not
’. and are called 
events .
Solution : Complementary .
Question: Two players , Sangeeta and Reshma , play a tennis match . It is known that the probability of Sangeeeta winning the match is 0.62 . Then the probability of Reshma winning the match is 
.
Solution : 0.38 [ The probability of Reshma’s winning 
]
Question: The probability of an event is greater than or equal to 
and less than or equal to 
.
Solution : 0 and 1
SECTION = B [ 1 or 2 Marks]
Question: A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 and these are equally likely outcomes . Find the probability that the arrow will point at any factor of 8 . [2015F]
Solution: The total number of possible outcome 
The number of factor of 8 
Question: If three different coins are tossed together, then find the probability of getting two heads . [2017C]
Solution : Total number of elementary events 
The favourable number of elementary events 
Question: One card is drawn from a well-shuffled deck of 52 cards . Find the probability of getting a spade . [SEBA 2018]
Solution: Total number of possible outcome 
The number of a spade 
.
Question: Cards marked with number 3 , 4 , 5 , ……… , 50 are placed in a box and mixed thoroughly . A card is drawn at random from the box . Find the probability that the selected card bears a perfect square number . [2016 Delhi]
Solution: Total number of elementary events 
.
The favourable number of elementary events 
[ 1 , 4 , 9 , 16 , 25 , 36 , 49]
P(getting a perfect square number) 
Question: Find the probability of getting the letter M in the word ‘‘ MATHEMATICS ’’ .
Solution: Total number of elementary events 
.
The favourable number of elementary events
P(getting the letter M) 
Question: A letter is chosen at random from the letter of the word ‘‘ PROBABILITY ’’ . Find the probability that it is not a vowel .
Solution: The total number of word
The number of ‘‘ not a vowel ’’ 
Question: A bag contains 3 red and 5 black balls . A ball is drawn at random from the bag . What is the probability that the drawn ball is not red ? [2017C Delhi]
Solution: Total number of balls
Question: What is the probability of getting a number less than 7 in a single throw of a die ?
Solution: Total number of possible outcome
Question: Gopi buys a fish from a shop for his aquarium . The shopkeeper takes out one fish at random from a tank containing 5 male fish and 8 female fish . What is the probability that the fish taken out is a male fish ?
Solution: Total number of fishes 
Question: It is given that a group of 3 students, the probability of 2 students not having the same birthday is 0.992 . What is the probability that the 2 students have the same birthday .
Solution: 2 students from a groups of 3 students not having the same birthday 
2 students from a group of 3 students having the same birthday 
Question: A card is drawn at random from a well shuffled pack of 52 playing cards . Find the probability of getting neither a red card nor a queen . [CBSE 2016]
Solution: Total number of elementary events .
The favourable number of elementary events 
.
P(getting neither a red nor a queen) 
SECTION = B [2 or 3 Marks]
Question: A bag contains 3 red balls and 5 black balls . A ball is drawn at random from the bag . What is the probability that the ball drawn is (i) red (ii) not red [SEBA 2019]
Solution: Total number of balls = 3 + 5 = 8
(i) P(getting the red balls) 
(ii) P(getting not red balls) 
Question: Two different dice are rolled simultaneously . Find the probability that the sum of numbers appearing on the two dice is 10 . [2014F]
Solution: Total number of possible outcome = 36
The favourable number of elementary events = 3 [ (4 , 6) , (5 , 5) , (6 , 4) ]
P(getting the sum of numbers appearing on the two dice is 10) 
Question: A die is thrown once . Find the probability of getting : [SEBA 2017]
(i) a prime number (ii) a number lying between 2 and 6 .
Solution: Total number of possible outcome = 6
(i) The favourable number of elementary events = 3 [ 2 , 3 , 5 ]
P(getting a prime number) 
(ii) The favourable number of elementary events = 3 [3 , 4 , 5 ]
P(getting a number lying between 2 and 6)
Question: One card is drawn from a well-shuffled deck of 52 cards . Find the probability of getting .
(i) a king of red colour (ii) a spade . (iii) a red face card [SEBA 2020]
Solution: Total number of possible outcome = 52
(i) The favourable number of elementary events = 2 [Hearts and diamonds are of red colour]
P(getting a king of red colour) 
(ii) The favourable number of elementary events = 13 [13 card of the spade]
P(getting a spade)
(iii) The favourable number of elementary events = 6 [2Kings , 2Queens and 2 jacks]
P(getting a spade) 
Question: A bag contains 5 white , 6 red and 4 green marbles . One marble is drawn at random from the bag . What the probability that the marble drawn is not red ? [SEBA 2013]
Solution: Total number of marbles 
P(not red marbles) 
Question: A bag contains a red ball , a blue ball and a yellow ball, all the balls being of the same size . Kritika takes out a ball from the bag without looking into it . What is the probability that she takes out the –
(i) yellow ball ? (ii) red ball ? (iii) blue ball ?
Solution: Total number of balls 
(i) P(getting yellow ball) 
(ii) P(getting red ball)
(iii) P(getting blue ball)
Question: Two different dice are tossed together . Find the probability of getting - [CBSE 2014]
(i) same number on both dice (i.e. a doublet) . (ii) a multiple of 3 as the sum .
Solution: Total number of possible outcome 
.
(i) The total number of elementary events 
P(getting the number on each die is even) 
(ii) The total number of elementary events = 12 .
P(getting a multiple of 3 as the sum) 
Question: From all the two digit numbers, a number is chosen at random . Find the probability that the chosen number is a multiple of 7 . [2017C]
Solution: The total number of possible outcome 
The favourable number of elementary events 
P(getting the number is a multiple of 7) 
Question: A number 
is selected at random from the numbers 1 , 2 , 3 and 4 . Another number 
is selected at random from the numbers 1 , 4 , 9 and 16 . Find the probability that product of and 
is less than 16 . [2016]
Solution: The total number of possible outcome = 16 .
The total number of elementary events 
P(getting the product of and is less than 16) 
Question: A bag contains 25 cards numbered from 1 to 25 . A card is drawn at random from the bag . Find the probability that the number on the drawn card is : [2015 Delhi]
(i) divisible by 3 or 5 . (ii) a perfect square number .
Solution: The total number of the cards = 25 .
(i) The favourable number of elementary events 
P( getting the number divisible by 3 or 5) 
(ii) The favourable number of elementary events 
P(getting a perfect square number) 
Question: A jar contains 24 marbles, some are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is ⋅ Find the number of blue balls in the jar.
Solution: Total number of marbles = 24.
Let, x be the number of green marbles .
Then the number of blue marbles = 24 – x .
A/Q, 
Thus, the number of blue marbles is 24 − 16 = 8.
Question: A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball, determine the number of blue balls in the bag.
Solution: Let, x be the number of blue balls .
and the total number of balls in the bag 
Probability of drawing a red ball 
Probability of drawing a blue ball 
A/Q, 
Therefore, the number of blue balls in the bag is 10.
Question: A box contains 12 balls out of which x are black. If one ball is drawn at random from the box, what is the probability that it will be a black ball ? If 6 more black balls are put in the box, the probability of drawing a black ball is now double of what it was before. Find 
.
Solution: Total number of balls initially = 12.
Number of black balls = x.
The probability of drawing a black ball 
Total number of balls = 12 + 6 = 18
Number of black balls = x + 6 .
The new probability of drawing a black ball 
A/Q, 
Therefore, the value of x is 3 .
SECTION = C [3 or 4 Marks]
Question: A lot consists of 144 ball pens of which 20 are defective and the others are good . Nuri will buy a pen if it is good, but will not buy if it is defective . The shopkeeper draws one pen at random and gives it to her . What is the probability that (i) She will buy it ? (ii) She will not buy it ? [SEBA 2016]
Solution: Total number of ball pens = 144 .
The number of defective ball pens = 20 .
The number of good ball pens = 144 – 20 =124
(i) P( getting a good ball pens) 
(ii) P(getting a defective ball pens) 
Question: All red face cards are removed from a pack of playing cards . The remaining cards were well shuffled and then a card is drawn at random from them . Find the probability that the drawn cards is :
(i) a red card (ii) a face card (iii) a card of clubs [2015 Delhi]
Solution: Total number of possible outcome 
[6 red face card are removed from the pack]
(i) The total number of a red card 
P(getting a red card) 
(ii) The total number of a face card = 
P(getting a face card) 
(iii) The total number of a card of clubs
P(getting a card of clubs) 
Question: Three different coins are tossed together .Find the probability of getting : [2016]
(i) exactly two heads (ii) at least two heads
Solution: Total number of possible outcome 
(i) The favourable number of elementary events 
P(getting the exactly two heads)
(ii) The favourable number of elementary events 
P(getting at least two heads) 
Question: Cards numbered 1 to 30 are put in a bag . A card is drawn at random from this bag . Find the probability that the number on the drawn card is : [CBSE 2014F]
(i) not divisible by 3 . (ii) a prime number greater than 7 . (iii) not a perfect square number .
Solution: Total number of possible outcome 
.
(i) The favourable number of elementary events 
P(not divisible by 3) 
(ii) The favourable number of elementary events 
P(getting a prime number greater than 7) 
(iii) The favourable number of elementary events 
P(not a perfect square number) 
Question: A piggy bank contains hundred 50 p coins , fifty Rs. 1 coins , twenty Rs. 2 coins and ten Rs. 5 coins .If it is equally likely that one of the coins will fall out when the bank is turned upside down , what is the probability that the coin (i) will be a 50 p coin ? (ii) will not be a Rs. 5 coin ?
Solution: Total number of coins 
(i) The total number of a 50 p coins = 100 .
P(getting a 50 p coin) 
(ii) The total number of a Rs. 5 coins 
P(getting a Rs. 5 coin) 
Question: A box contains cards, number from 1 to 90 . A card is drawn at random from the box. Find the probability that the selected card bears : (i) a perfect square number (ii) a prime number between 8 to 40 .
Solution: Total number of possible outcome 
.
(i) The total number of a perfect square number from 1 to 90 = 9 [1,4,9,16,25,36,49,64,81]
P(getting a perfect square number) 
(ii) The total number of a prime number between 8 to 40 = 8 [11,13,17,19,23,29,31,37]
P(getting a prime number between 8 to 40) 
Question: Five cards – the ten , jack , queen , king and ace of diamonds , are well-shuffled with their face downwards . One card is then picked up at random .
(i) What is the probability that the card is the queen ? (ii) If the queen is drawn and put aside, what is the probability that the second card picked up is (a) an ace ? (b) a queen ?
Solution: The total number of possible outcome = 5 [ten, jack ,queen, king and ace]
(i) The number of elementary events = 1 [ Queen only]
P( getting the queen) 
(ii) The total number of elementary events = 4 [ The queen has removed]
(a) P(getting an ace) 
(b) P(getting a queen) 
Question: A box contains cards bearing numbers from 6 to 70 . If one card is drawn at random from the box , find the probability that it bears : [CBSE 2015F]
(i) a one digit number (ii) a number divisible by 5 . (iii) an odd number less than 30 (iv) a composite number between 50 and 70 .
Solution: Total number of possible outcome 
(i) Total number of a one digit number 
[6 , 7 , 8 , 9]
P(getting a one digit number) 
(ii) Total number of a number divisible by 5 [10,15,20,25,30,35,40,45,50,55,60,65,70]
P(getting a number divisible by 5) 
(iii) Total number of an odd number less than 30 
[7,9,11,13,15,17,19,21,23,25,27,29]
P(getting an odd number less than 30) 
.
(iv) Total number of a composite number between 50 and 70 
[ Composite number between 50 and 70 are 51,52,54,56,57,58,60,62,63,64,65,68,69,70]
P(getting a composite number between 50 and 70) 
Question: A box contains 90 discs which are numbered from 1 to 90 . If one disc is drawn at random from the box , find the probability that it bears (i) a two-digit number (ii) a perfect square number (iii) a number divisible by 5 .
Solution : Total number of discs in the box 
(i) The number of a two-digit number in box 
.
P(getting a two-digit number) 
(ii) The number of a perfect square number in box 
P(getting a perfect square number) 
(iii) The number of discs divisible by 5 
P(getting a number divisible by 5) 
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