Home Class 10 Worksheets Probability

Chapter 14: Probability

Overview

This page provides comprehensive Chapter 14: Probability - Assertion Reason Worksheet - SJMaths. Assertion and Reason type questions for Class 10 Probability. Practice for CBSE Board Exams.

Assertion-Reason Worksheet

Back to Worksheets

Directions:

In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

  • (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • (B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
  • (C) Assertion (A) is true but Reason (R) is false.
  • (D) Assertion (A) is false but Reason (R) is true.
  1. Question 1:
    Assertion (A): The probability of an event $E$ is a number $P(E)$ such that $0 \le P(E) \le 1$.
    Reason (R): The probability of a sure event is 1 and that of an impossible event is 0.
    (A)
    (B)
    (C)
    (D)
    Solution: (B)
    Step 1: A is true (definition of probability range).
    Step 2: R is true (properties of sure/impossible events).
    Step 3: R is an example/property but not the complete explanation of why probability is between 0 and 1 (which comes from favorable outcomes $\le$ total outcomes). So B is correct.
  2. Question 2:
    Assertion (A): If $P(E) = 0.07$, then the probability of 'not E' is 0.93.
    Reason (R): $P(E) + P(\text{not } E) = 1$.
    (A)
    (B)
    (C)
    (D)
    Solution: (A)
    Step 1: $P(\text{not } E) = 1 - 0.07 = 0.93$. A is true.
    Step 2: R is the correct complementary rule used.
  3. Question 3:
    Assertion (A): When a die is thrown, the probability of getting a number less than 7 is 1.
    Reason (R): Getting a number less than 7 on a die is a sure event.
    (A)
    (B)
    (C)
    (D)
    Solution: (A)
    Step 1: Outcomes are {1, 2, 3, 4, 5, 6}. All are less than 7. A is true.
    Step 2: Since it always happens, it is a sure event. R explains A.
  4. Question 4:
    Assertion (A): A card is drawn from a well-shuffled deck of 52 cards. The probability of getting a face card is 3/13.
    Reason (R): There are 12 face cards in a deck of 52 cards.
    (A)
    (B)
    (C)
    (D)
    Solution: (A)
    Step 1: Face cards (J, Q, K) in 4 suits = 12. Probability $= 12/52 = 3/13$. A is true.
    Step 2: R provides the count used in calculation.
  5. Question 5:
    Assertion (A): In a leap year, the probability that there are 53 Sundays is 2/7.
    Reason (R): A leap year has 366 days.
    (A)
    (B)
    (C)
    (D)
    Solution: (A)
    Step 1: 366 days = 52 weeks + 2 extra days. Extra days can be (Sun,Mon), (Mon,Tue)... (Sat,Sun). Total 7 pairs. 2 contain Sunday. Prob = 2/7. A is true.
    Step 2: R states the number of days, which is the basis of the calculation.
  6. Question 6:
    Assertion (A): If a box contains 5 white, 2 red and 4 black marbles, then the probability of not drawing a white marble is 5/11.
    Reason (R): $P(\text{not white}) = 1 - P(\text{white})$.
    (A)
    (B)
    (C)
    (D)
    Solution: (D)
    Step 1: Total $= 5+2+4 = 11$. $P(\text{white}) = 5/11$.
    Step 2: $P(\text{not white}) = 1 - 5/11 = 6/11$. Assertion says 5/11, which is false.
    Step 3: R is true.
  7. Question 7:
    Assertion (A): When two coins are tossed simultaneously, the probability of getting no tail is 1/4.
    Reason (R): The probability of getting exactly one tail is 1/2.
    (A)
    (B)
    (C)
    (D)
    Solution: (B)
    Step 1: Outcomes: HH, HT, TH, TT. No tail means HH (1 outcome). Prob = 1/4. A is true.
    Step 2: Exactly one tail: HT, TH (2 outcomes). Prob = 2/4 = 1/2. R is true.
    Step 3: R is a correct statement but does not explain A.
  8. Question 8:
    Assertion (A): The probability of winning a game is 0.4, then the probability of losing it is 0.6.
    Reason (R): $P(E) + P(\text{not } E) = 1$.
    (A)
    (B)
    (C)
    (D)
    Solution: (A)
    Step 1: $P(\text{Lose}) = 1 - P(\text{Win}) = 1 - 0.4 = 0.6$. A is true.
    Step 2: R is the rule used.
  9. Question 9:
    Assertion (A): If a die is thrown, the probability of getting a number greater than 6 is 1.
    Reason (R): Probability of an impossible event is zero.
    (A)
    (B)
    (C)
    (D)
    Solution: (D)
    Step 1: Getting > 6 on a die is impossible. Probability is 0. A is false.
    Step 2: R is true.
  10. Question 10:
    Assertion (A): Three coins are tossed together. The probability of getting at least two heads is 1/2.
    Reason (R): Total outcomes are 8: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT.
    (A)
    (B)
    (C)
    (D)
    Solution: (A)
    Step 1: At least 2 heads: HHH, HHT, HTH, THH (4 outcomes).
    Step 2: Probability $= 4/8 = 1/2$. A is true.
    Step 3: R lists the sample space used for counting. R explains A.
Previous Worksheet Next Worksheet