LIWA

Probability

CBSE Class 10 · Maths · Chapter 14

Past board exam questions

CBSE 2027 sample paper · 1 mark

A letter from the word INDEPENDENCE is selected at random. What is the probability that the letter selected is a vowel which occurs the maximum number of times in the given word?

  1. (1)/(12)
  2. (1)/(4)
  3. (1)/(3)
  4. (5)/(12)
Show answer
(1)/(3)

CBSE 2027 sample paper · 1 mark

T-shirts marked with numbers 4 to 99 are placed in a box. Gunika is fond of numbers. She randomly takes out a T-shirt from this box. The probability that she gets a T-shirt marked with a number that is either a perfect square or a perfect cube is:

  1. (1)/(12)
  2. (1)/(32)
  3. (11)/(96)
  4. (5)/(48)
Show answer
(5)/(48)

CBSE 2027 sample paper · 1 mark

Two dice are rolled simultaneously. The probability of getting number less than 4 on each die is:

  1. (1)/(4)
  2. (1)/(9)
  3. (1)/(36)
  4. (1)/(6)
Show answer
(1)/(4)

CBSE 2027 sample paper · 1 mark

2 cards of diamonds and 4 cards of spades are missing from a pack of 52 cards. A card is drawn at random from this pack. The probability of getting a card of heart is:

  1. (13)/(52)
  2. (13)/(46)
  3. (11)/(52)
  4. (11)/(46)
Show answer
(13)/(46)

CBSE 2027 sample paper · 1 mark

ASSERTION (A): The probability of getting number 8 on rolling a die is zero (0) REASON (R): The probability of an impossible event is zero (0)

  1. Both Assertion (A) and Reason (R) are true and (R) is the correct explanation of Assertion (A).
  2. Both Assertion (A) and Reason (R) are true but (R) is not the correct explanation of Assertion (A).
  3. Assertion (A) is true but Reason (R) is false.
  4. Assertion (A) is false but Reason (R) is true.
Show answer
Both Assertion (A) and Reason (R) are true and (R) is the correct explanation of Assertion (A).

CBSE 2027 sample paper · 2 marks

Two dice are thrown simultaneously. Find the probability that the product of the numbers appearing on them is a prime number.

Show answer
Total number of outcomes = 36. The product is prime only when one die shows 1 and the other a prime: (1, 2), (1, 3), (1, 5), (2, 1), (3, 1), (5, 1) — 6 outcomes. P(product is prime) = (6)/(36) = (1)/(6).

CBSE 2027 sample paper · 4 marks

A labourer prints 400 T-shirts in a day. The supervisor checked the T-shirts and found that 312 prints were good, 54 prints were with minor defects and rest of the prints were of major defects. Harish, a customer will buy a T-shirt only if it is good but a trader will buy, if it has no major defect. If a random T-shirt is picked, then (i) find the probability that Harish will buy a T-shirt. (1) (ii) find the probability that a trader will buy the T-shirt. (1) (iii)(A) find the probability that the T-shirt is not good. (2) OR (iii)(B) find the probability that neither Harish nor trader buy the T-shirt. (2)

Show answer
Total = 400; good = 312; minor defects = 54; major defects = 400 − 312 − 54 = 34. (i) P(Harish buys) = (312)/(400) = (39)/(50). (ii) P(trader buys) = (312 + 54)/(400) = (366)/(400) = (183)/(200). (iii)(A) P(not good) = 1 - (312)/(400) = (88)/(400) = (11)/(50). OR (iii)(B) Neither buys only when the print has a major defect: P = (400 - 312 - 54)/(400) = (34)/(400) = (17)/(200).

CBSE 2026 board paper · 1 mark

Which of the following cannot be the probability of an event ?

  1. 1
  2. (1)/(2)
  3. 0.75
  4. -1
Show answer
-1