THE GOAL • CBSE CLASS 10

PROBABILITY

Chapter 14 • Basic Mathematics • 2025 PYQs

CBSE 2025 Basic Mathematics Previous Year Questions Chapter-wise Collection

Chapter 14: Probability

Unique Previous Year Questions extracted from the CBSE Class 10 Basic Mathematics 2025 question paper sets. Repetitive questions have been removed while retaining the major question types and variations.

I

Multiple Choice Questions

1. Conceptual – Sure Event
1 Mark
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. Basic Complementary Probability
1 Mark
If the probability of happening of an event is \(57\%\), then the probability of non-happening of the event is:
(A) \(0.43\)
(B) \(0.57\)
(C) \(53\%\)
(D) \(\frac{1}{57}\)
Set 430/6/2
3. Balls – Complementary Event
1 Mark
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:
(A) \(\frac{1}{11}\)
(B) \(\frac{3}{14}\)
(C) \(\frac{11}{14}\)
(D) \(\frac{3}{11}\)
Set 430/1/2
4. Dice – Doublet
1 Mark
In an experiment of throwing a pair of dice, the probability of not getting a doublet is:
(A) \(\frac{1}{6}\)
(B) \(\frac{5}{6}\)
(C) \(\frac{1}{5}\)
(D) \(\frac{1}{30}\)
Set 430/1/3
5. Dice – Total Outcomes
1 Mark
The total number of outcomes in the experiment of simultaneous throw of three dice is:
(A) 6
(B) 18
(C) 36
(D) 216
Set 430/2/1
6. Dice – Sum at Least 9
1 Mark
A pair of dice is thrown simultaneously. Let \(E\) denote the event that the sum of numbers obtained on both dice is at least 9. The number of outcomes in favour of event \(E\) is:
(A) 4
(B) 6
(C) 10
(D) 26
Set 430/3/1
7. Dice – Sum More Than 9
1 Mark
Two dice are rolled together. The probability of getting a sum more than 9 is:
(A) \(\frac{5}{6}\)
(B) \(\frac{5}{18}\)
(C) \(\frac{1}{6}\)
(D) \(\frac{1}{2}\)
Set 430/6/3
8. Dice – Algebraic Relation
1 Mark
Two dice are rolled together. The probability of getting an outcome \((a,b)\) such that \(b=2a\), is:
(A) \(\frac{1}{6}\)
(B) \(\frac{1}{12}\)
(C) \(\frac{1}{36}\)
(D) \(\frac{1}{9}\)
Set 430/6/2
9. Coins – Exactly One Tail
1 Mark
Three coins are tossed together. The probability that only one coin shows tail is:
(A) \(\frac{1}{2}\)
(B) \(\frac{3}{8}\)
(C) \(\frac{7}{8}\)
(D) \(1\)
Set 430/4/1
10. Coins – At Least One Head
1 Mark
Three coins are tossed together. The probability that at least one head comes up is:
(A) \(\frac{3}{8}\)
(B) \(\frac{7}{8}\)
(C) \(\frac{1}{8}\)
(D) \(\frac{3}{4}\)
Set 430/6/3
11. Cards – Specific Number
1 Mark
A card is drawn at random from a well shuffled deck of 52 playing cards. The probability that the drawn card shows number \(9\) is:
(A) \(\frac{1}{26}\)
(B) \(\frac{4}{13}\)
(C) \(\frac{1}{52}\)
(D) \(\frac{1}{13}\)
Set 430/4/1
12. Cards – Lost Card
1 Mark
A black card is lost from a deck of 52 playing cards. The remaining cards are shuffled and one card is drawn at random. The probability that the drawn card is the king of hearts is:
(A) \(\frac{1}{52}\)
(B) \(\frac{1}{4}\)
(C) \(\frac{1}{51}\)
(D) \(\frac{1}{26}\)
Set 430/5/2
13. Decimal / Percent Relation
1 Mark
If \(E\) is an event such that \(P(E)=1\%\), then \(P(\text{not }E)\) is equal to:
(A) \(0.09\)
(B) \(0.99\)
(C) \(\frac{1}{99}\)
(D) \(0.90\)
Set 430/5/2
II

Assertion – Reason Question

14. Complementary Probability
1 Mark
Assertion (A): If \(E\) is an event such that \(P(E)=\frac{1}{999}\), then \(P(\text{not }E)=0.001\).
Reason (R): \[ P(E)+P(\text{not }E)=1. \]
Set 430/4/1
III

Very Short Answer Type Questions

15. Figure Based – Geometric Probability
2 Marks
A coin is dropped at random on the rectangular region shown in the figure. The rectangle measures \(3\,m\times2\,m\), and a circle of radius \(0.7\,m\) lies inside it.
What is the probability that the coin will land inside the circle?
Set 430/4/1
16. Dice – Two Conditions
2 Marks
A die is thrown twice. Find the probability that:
(i) the difference between the two numbers obtained is \(3\).
(ii) the sum of the numbers obtained is \(8\).
Set 430/4/1
17. Algebraic Probability – Marbles
2 Marks
A bag contains 40 marbles out of which some are white and others are black. If the probability of drawing a black marble is \(\frac{3}{5}\), find the number of white marbles.
Set 430/5/1
18. Cards – Prime and Perfect Square
2 Marks
In a pre-primary class, a teacher put cards numbered \(20\) to \(59\) in a bowl. A student picked up a card at random and read the number.
(i) Find the probability that the number read was a prime number.
(ii) Find the probability that the number read was a perfect square.
Set 430/5/1
19. Numbered Discs – Two Conditions
2 Marks
A box contains 120 discs, numbered from \(1\) to \(120\). If one disc is drawn at random, find the probability that:
(i) it bears a two-digit number.
(ii) the number is a perfect square.
Set 430/6/2
IV

Short Answer Type Questions

20. Multi-Lot Pen Problem
3 Marks
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.
(i) What is the probability that the customer will not buy a pen drawn at random?
(ii) Another lot of 100 pens containing 80 good pens is mixed with the previous lot. What is the probability that the customer will buy a pen drawn at random from the entire lot?
Set 430/1/1
21. Figure Based – Spinning Wheel
3 Marks
A game of chance consists of spinning a wheel which comes to rest at one of the numbers from \(1\) to \(10\), as shown in the figure. Find 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 \(4\)
Set 430/2/1
22. Mixed Marbles
3 Marks
A box contains 6 blue, 4 white and 8 red marbles. A marble is drawn at random from this box. Find the probability that the marble so drawn is:
(i) white
(ii) white or red
(iii) not red
Set 430/3/1