Probability: Class 10 Previous Year Questions

Probability questions asked in CBSE board exams

Repeated questions first. Open the free app to see each question as it appeared in the paper, with its marking scheme.

1. Prove that a line drawn parallel to one side of a triangle to intersect the other two sides in distinct points divides the other two sides in the same ratio. Hence, in the figure given below, prove that = where LM || CB and LN || CD.
   Board 20255 markslong answerRepeated: 2023,2024,2025
2. (A) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove that the other two sides are divided in the same ratio. OR (B) In the given figure PA, QB and RC are each perpendicular to AC. If AP = x, …
   Board 20245 markslong answerRepeated: 2023,2024,2025
3. Two dice are thrown at the same time. Determine the probability that the (i) sum of the numbers on the two dice is 5, and (i) difference of the numbers on the two dice is 3. 4x5=20 32· 33. (·) 4,200 () 600c10c 34. (·) () 3.6m 90 cm
   Board 20263 marksshort answerRepeated: 2025,2026
4. A die is thrown once. Probability of getting a number other than 3 is : (a) (b) (c) (d) 1 Directions : Question numbers 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled as Assertion (A) and the other is labelled as Rea…
   Board 20261 markAssertion-ReasonRepeated: 2023,2026
5. Two dice are thrown at the same time. Determine the probability that the difference of the numbers on the two dice is 2.
   Board 20253 marksshort answerRepeated: 2025,2026
6. Page 9 13. A box contains cards numbered 6 to 55. A card is drawn at random from the box. The probability that the drawn card has a number which is a perfect square, is 1 (A) 7 50 (B) 7 55 (C) 1 10 (D) 5 49 Page 10 14.    ,  O    …
   Board 20241 markMCQRepeated: 2023,2024
7. A bag contains 100 cards numbered 1 to 100. A card is drawn at random from the bag. What is the probability that the number on the card is a perfect cube ? (a) 20 1 (b) 50 3 (c) 25 1 (d) 100
   Board 20231 markMCQRepeated: 2023,2024
8. Assertion (A) : The probability that a leap year has 53 Mondays is Reason (R) : The probability that a non-leap year has 53 Mondays is
   Board 20261 markAssertion-Reason
9. Two dice of different colours are thrown at the same time. Write down all the possible outcomes. What is the probability that : (i) same number appears on both the dice ? (i) different number appears on both the dice ?
   Board 20263 marksshort answer
10. A card is selected at random from a deck of 52 playing cards. The probability of it being a red face card is : (A) (B) (C) (D)
    Board 20251 markMCQ
11. Assertion (A) : The probability of selecting a number at random from the numbers 1 to 20 is 1. Reason (R): For any event E, if P(E) = 1, then E is called a sure event.
    Board 20251 markAssertion-Reason
12. The probability of drawing an even prime number out of numbers from 1 to 30 is : (A) (B) (C) (D)
    Board 20251 markMCQ
13. | P a g e 37. Rahul is a lucky charm for his cricket team. He has a jar of cards with numbers from 10 to 74. Before each match, he draws a card from the jar. If the card bears an even number, the team wins. If the number is even and divisible by 5, they win by…
    Board 20254 marksshort answer
14. In a cricket match, a batsman hits the boundary 7 times out of the 42 balls he plays. The probability of his not hitting a boundary is : (A) (B) (C) (D)
    Board 20251 markMCQ
15. In a pack of 52 playing cards one card is lost. From the remaining cards, a card is drawn at random. Find the probability that the drawn card is queen of heart, if the lost card is a black card.
    Board 20242 marksshort answer
16. Two dice are rolled together. The probability of getting sum of numbers on the two dice as 2, 3 or 5, is : 11 (b) (a) (c) (d) 36 36 36
    Board 20241 markMCQ
17. Two dice are rolled together. The probability of getting the sum of the two numbers to be more than 10, is 1 (A) 1 9 (B) 1 6 (C) 7 12 (D) 1 12 1
    Board 20241 markMCQ
18. From the data 1, 4, 7, 9, 16, 21, 25, if all the even numbers are removed, then the probability of getting at random a prime number from the remaining is : 2- (d) (a) (b) (c)
    Board 20241 markMCQ
19. Page 23 38. In a survey on holidays, 120 people were asked to state which type of transport they used on their last holiday. The following pie chart shows the results of the survey. Observe the pie chart and answer the following questions : (i) If one person i…
    Board 20244 marksshort answer
20. If the probability of a player winning a game is 0.79, then the probability of his losing the same game is : (a) 1.79 (b) 0.31 (c) 0.21% (d) 0.21
    Board 20241 markMCQ

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