Assertion (A): If probability of happening of an event is $0.2p$, $p 0$, then $p$ can't be more than $5$. R…

Question

Assertion (A): If probability of happening of an event is $0.2p$, $p > 0$, then $p$ can't be more than $5$.

Reason (R): $P(\bar{E}) = 1 - P(E)$ for an event $E$.

Select the correct answer from the options (A), (B), (C) and (D) as given below:

Accepted Answer

## Model Answer **(A)** — Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A). Since $P(E) \leq 1$, we need $0.2p \leq 1$, giving $p \leq 5$. This follows directly from the complement rule $P(\bar{E}) = 1 - P(E)$, which ensures $0 \leq P(E) \leq 1$. ## Explanation The assertion is verified: $0.2p \leq 1 \Rightarrow p \leq 5$, so $p$ cannot exceed 5. The reason (complement rule) is the fundamental property that bounds all probabilities between 0 and 1, which is exactly why the assertion holds — making R the correct explanation of A. Choose option **(A)**.

Mathematics — Standard (041) — CBSE Class 10 board question