CHAPTER 14 : PROBABILITY
CBSE Class 10 Mathematics — PYQs 2026 | Basic + Standard
BASIC QUESTION PAPER 2026
SECTION A : MULTIPLE CHOICE QUESTIONS (1 Mark Each)
1.
In a random experiment of throwing a die, which of the following
is a
sure event?
(A) Getting a number between 1 and 6
(B) Getting an odd number < 7
(C) Getting an even number < 7
(D) Getting a natural number < 7
[Set: 430/1/1]
2.
A bag contains 3 red, 4 white and 7 green balls.
A ball is drawn at random. The probability that the ball
drawn is
not of red colour is:
[Sets: 430/1/2, 430/2/2]
3.
The total number of outcomes in the experiment of
simultaneous throw of three dice is:
(A) 6
(B) 18
(C) 36
(D) 216
[Sets: 430/2/1, 430/2/2, 430/2/3]
4.
In an experiment of throwing a pair of dice, the probability
of
not getting a doublet is:
[Set: 430/1/3]
5.
A pair of dice is thrown once. Let event \(E\) represent
“the sum of numbers on two dice is
at least 9”.
The number of outcomes in favour of event \(E\) is:
(A) 4
(B) 6
(C) 10
(D) 26
[Sets: 430/3/1, 430/3/2, 430/3/3]
SECTION B : SHORT ANSWER QUESTIONS (3 Marks Each)
1.
Type A: Defective Items (Pens Lot)
A lot consists of 200 pens of which 180 are good and the rest
are defective. A customer will buy a pen if it is not defective.
The shopkeeper draws a pen at random.
(i)
What is the probability that the customer will
not buy it?
(ii)
Another lot of 100 pens containing 80 good pens is mixed
with the previous lot. The shopkeeper now draws one pen
at random from the entire lot. What is the probability that
the customer will buy the pen?
[Sets: 430/1/1, 430/1/2, 430/1/3]
2.
Type B: Game of Chance (Spinning Wheel)
A wheel is divided into 10 equal sectors numbered 1 to 10.
What is the probability that the wheel stops at:
(i) a prime number greater than 2?
(ii) an odd number less than 9?
(iii) a multiple of 4?
[Sets: 430/2/1, 430/2/2, 430/2/3]
3.
Type C: Coloured Marbles
A box contains 6 blue, 4 white and 8 red marbles.
A marble is drawn at random. Find the probability that
the marble drawn is:
(i) white
(ii) white or red
(iii) not red
[Sets: 430/3/1, 430/3/2, 430/3/3]
STANDARD QUESTION PAPER 2026
SECTION A : MULTIPLE CHOICE QUESTIONS (1 Mark Each)
1.
Two different dice are rolled together. The probability that
both the obtained numbers are less than 4, is:
(A) \(\dfrac{2}{9}\)
(B) \(\dfrac{7}{36}\)
(C) \(\dfrac{1}{4}\)
(D) \(\dfrac{2}{3}\)
[Set 30/4/1 Q10, Set 30/4/2 Q6]
2.
Two dice are rolled together. The probability that the sum
of the numbers obtained is at most 12, is:
(A) \(1\)
(B) \(0\)
(C) \(\dfrac{1}{2}\)
(D) \(\dfrac{35}{36}\)
[Set 30/4/3 Q17]
3.
Two dice are rolled together. The probability that the sum
of the numbers obtained is divisible by 6, is:
(A) \(\dfrac{1}{6}\)
(B) \(\dfrac{11}{36}\)
(C) \(\dfrac{1}{12}\)
(D) \(\dfrac{1}{4}\)
[Set 30/3/1 Q5, Set 30/3/3 Q2]
4.
Two dice are rolled together. The probability of getting
an outcome \((x,y)\) where \(x>y\), is:
(A) \(\dfrac{5}{12}\)
(B) \(\dfrac{5}{6}\)
(C) \(1\)
(D) \(0\)
[Set 30/5/3 Q18]
5.
A die is thrown once. The probability of getting a number
other than 3 is:
(A) \(\dfrac{1}{6}\)
(B) \(\dfrac{3}{6}\)
(C) \(\dfrac{5}{6}\)
(D) \(1\)
[Set 30/1/1 Q18]
6.
Three coins are tossed together. The probability of getting
exactly one head, is:
(A) \(\dfrac{1}{8}\)
(B) \(\dfrac{3}{4}\)
(C) \(\dfrac{1}{2}\)
(D) \(\dfrac{3}{8}\)
[Set 30/3/2 Q9]
7.
The probability for a randomly selected number out of
\(1,2,3,4,\ldots,25\) to be a composite number is:
(A) \(\dfrac{15}{25}\)
(B) \(\dfrac{10}{25}\)
(C) \(\dfrac{11}{25}\)
(D) \(\dfrac{9}{25}\)
[Set 30/2/1 Q18, Set 30/2/2 Q17, Set 30/2/3 Q18]
8.
Meena calculates that the probability of her winning the
first prize in a lottery is \(0.08\). If a total of 800 tickets
were sold, the number of tickets bought by her is:
(A) 64
(B) 640
(C) 100
(D) 10
[Set 30/5/1 Q16, Set 30/5/2 Q12, Set 30/5/3 Q3]
9.
Which of the following cannot be the probability of an event?
(A) \(\dfrac{39}{100}\)
(B) \(\dfrac{0.001}{20}\)
(C) \(\dfrac{10}{0.2}\)
(D) \(10\%\)
[Set 30/5/1 Q10, Set 30/5/2 Q17, Set 30/5/3 Q13]
10.
For an event \(E\),
\(P(E)+P(\bar{E})=x\).
Then the value of \(x^2-3\) is:
(A) \(-2\)
(B) \(2\)
(C) \(1\)
(D) \(-1\)
[Set 30/1/2 Q4]
11.
A card is drawn at random from a well-shuffled deck of
52 playing cards. The probability that it is either a ten
or a king is:
(A) \(\dfrac{1}{26}\)
(B) \(\dfrac{2}{13}\)
(C) \(\dfrac{1}{13}\)
(D) \(\dfrac{8}{26}\)
[Set 30/5/1 Q11, Set 30/5/2 Q7]
SECTION B : ASSERTION–REASON QUESTIONS (1 Mark Each)
1.
Assertion (A):
If probability of happening of an event is \(0.2p\),
\(p>0\), then \(p\) can’t be more than 5.
Reason (R):
\(P(\bar{E})=1-P(E)\) for an event \(E\).
[Set 30/4/1 Q19, Set 30/4/2 Q20,
Set 30/5/2 Q20, Set 30/5/3 Q19]
2.
Assertion (A):
The probability that a leap year has 53 Mondays is
\(\dfrac{2}{7}\).
Reason (R):
The probability that a non-leap year has 53 Mondays is
\(\dfrac{5}{7}\).
[Set 30/1/1 Q19, Set 30/1/2 Q19]
SECTION C : VERY SHORT ANSWER QUESTIONS (2 Marks Each)
1.
A bag contains 25 balls. Some of them are yellow and others
are green. One ball is drawn at random. If the probability of
getting a green ball is \(\dfrac{3}{5}\), then find the number
of yellow balls.
[Set 30/5/1 Q25, Set 30/5/2 Q24, Set 30/5/3 Q23]
SECTION D : SHORT ANSWER QUESTIONS (3 Marks Each)
1.
A bag contains 30 balls out of which \(m\) number of balls
are blue in colour.
(i)
Find the probability that a ball drawn at random from
the bag is not blue.
(ii)
If 6 more blue balls are added in the bag, then the
probability of drawing a blue ball will be
\(\dfrac{4}{5}\) times the probability of drawing a blue
ball in the first case. Find the value of \(m\).
[Set 30/4/1 Q30, Set 30/4/2 Q29, Set 30/4/3 Q27]
2.
Two dice of different colours are thrown at the same time.
Write down all the possible outcomes.
(i)
What is the probability that the same number appears
on both the dice?
(ii)
What is the probability that different numbers appear
on both the dice?
[Set 30/1/1 Q31]
3.
Two dice are thrown at the same time. Determine the
probability that:
(i)
the sum of the numbers on the two dice is 5.
(ii)
the difference of the numbers on the two dice is 3.
[Set 30/2/2 Q28]
4.
Two different dice are thrown together. Find the probability
that the numbers obtained have:
(i)
even sum
(ii)
even product
[Set 30/2/3 Q30]
SECTION E : CASE STUDY QUESTION (4 Marks)
Playing Cards
A group of friends wanted to play cards with two identical
packs together. While shuffling the cards, three cards are
dropped. Rest of the cards are shuffled and one card is
drawn at random.
Assuming that the dropped cards were a queen of hearts,
a ten of spades and an ace of clubs:
(i)
Find the probability that the drawn card is a face card.
(1 Mark)
(ii)
Find the probability that the drawn card is either a king
or a queen.
(1 Mark)
(iii) (a)
Do you think that the probability of getting a queen was
higher if none of the cards were dropped? Justify your answer.
(2 Marks)
OR
(iii) (b)
Find the probability that the drawn card is a jack.
Compare it with the probability when none of the cards
were dropped. In which case is the probability of getting
a jack higher?
(2 Marks)
[Set 30/3/1 Q37, Set 30/3/2 Q36, Set 30/3/3 Q38]