Question

Assertion (A) : If probability of happening of an event is 0.2p, p $\gt $ 0, then p can’t be more than 5.
Reason (R) : P( \(\overline{E}\) ) = 1 – P(E) for an event E.

• 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 Assertion (A).
• C. Assertion (A) is true, but Reason (R) is false.
• D. Assertion (A) is false, but Reason (R) is true.

Hint:

To test if a Reason is the correct explanation, read the Assertion, add "BECAUSE", and then read the Reason.
"p cannot be more than 5 BECAUSE the probability of the complementary event is 1 - P(E)."
This lacks direct logical coherence, showing that (R) is not the explanation for (A).

Answer 1

The Correct Option is B

Step 1: Use the maximum-probability boundary for Assertion (A).
Since probability can never exceed $1$, we need $0.2p \le 1$, which gives $p \le 5$. So Assertion (A) is a true statement.
Step 2: Check Reason (R) on its own merit.
The complement rule $P(\overline{E}) = 1 - P(E)$ is a standard, always-true result, so Reason (R) is also true.
Step 3: Check whether R actually explains A.
Assertion (A) was proved purely from the rule $P(E) \le 1$; the complement formula in Reason (R) was never needed to reach that conclusion. So R, though true, does not explain A.
\[ \boxed{\text{Option (B)}} \]