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 \(p\) cannot be more than 5 BECAUSE the probability of a complementary event is \(1 - P(E)\)."
This combined statement does not make logical sense. This confirms that the Reason is not the correct explanation of the Assertion!

Answer 1

The Correct Option is B

Step 1: Test the Assertion using a boundary value.
If \(p = 5\), then \(P(E) = 0.2 \times 5 = 1\), the largest possible probability, a certain event, so this is still allowed. If p were any bigger than 5, \(P(E)\) would exceed 1, which is impossible for any probability.
Step 2: Confirm the Assertion is true.
So p cannot be more than 5, and Assertion (A) is true.
Step 3: Check the Reason on its own.
Reason (R) states \(P(\overline{E}) = 1 - P(E)\), this is a standard, always-true rule for complementary events, so Reason (R) is also true.
Step 4: Decide if R explains A.
The bound on p came purely from the rule \(P(E) \le 1\), not from the complement rule \(P(\overline{E}) = 1 - P(E)\), so R, though true, does not explain A. This matches option (B).
\[ \boxed{\text{Option (B)}} \]