Q1. [1]
Assertion (A): In a cricket match, a batsman hits a boundary 9 times out of 45 balls he plays. The probability that in a given ball, he does not hit the boundary is $\dfrac{4}{5}$.
Reason (R): $P(E) + P(\text{not } E) = 1$
- A Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
- B Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
- C Assertion (A) is true, but Reason (R) is false.
- D Assertion (A) is false, but Reason (R) is true.
Previously asked in CBSE board exam
2024 30/3/1 Q20
Generated by claude-sonnet-4-6 · 2026-06-15 10:29 · grounding rag
Model Answer
Option A is correct. P(hitting boundary) = 9/45 = 1/5, so P(not hitting boundary) = 1 − 1/5 = 4/5. Assertion (A) is true, and Reason (R) — $P(E) + P(\text{not }E) = 1$ — is the correct explanation for it.
Source: Chapter 14, Section 14.1
Explanation
- First verify the Assertion: 9 boundaries in 45 balls → P(boundary) = 9/45 = 1/5; P(not boundary) = 1 − 1/5 = 4/5 ✓
- The Reason states the complementary event rule, which is exactly the formula used to get the answer → it is the correct explanation.
- So both A and R are true, and R correctly explains A → Option A.
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