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 easily check if the Reason is the correct explanation for the Assertion, read the Assertion statement, insert the word "BECAUSE", and then read the Reason statement:
"If the probability of an event is \(0.2p\), then \(p \le 5\) BECAUSE the probability of the complementary event is \(1 - P(E)\)."
This combined statement does not make logical sense, showing that the Reason is not the correct explanation!

Answer 1

The Correct Option is B

Step 1: Check the Assertion using the basic bound on probability.
Since $0\le P(E)\le1$ and $P(E)=0.2p$, we need $0.2p\le1$, giving $p\le5$. So Assertion (A) is true.
Step 2: Check the Reason on its own.
$P(\overline{E})=1-P(E)$ is a standard, always-true formula for complementary events, so Reason (R) is true.
Step 3: Test if the Reason actually explains the Assertion.
Reading it as "$p$ cannot exceed 5 BECAUSE $P(\overline{E})=1-P(E)$" does not logically connect, since the bound on $p$ came only from $P(E)\le1$, not from the complement formula.
Step 4: Conclude.
Both statements are true, but (R) does not explain (A), matching option (B).
\[ \boxed{\text{Option (B)}} \]