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(barE) = 1 - P(E)` for an event E.

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

• Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (А).

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

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

Answer 1

Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (А).

Explanation:

Probability of any event E always lies between 0 and 1 inclusive (0 ≤ P(E) ≤ 1).

The sum of probability of occurrence and non-occurrence of an event is 1.

Assertion (A): Given P(E) = 0.2p.

Since P(E) ≤ 1:

0.2p ≤ 1

`p ≤ 1/0.2`

p ≤ 5

So, p cannot be more than 5. (A) is true.

Reason (R): It is a fundamental property of probability that `P(E) + P(barE) = 1`, so `P(barE) = 1 - P(E)`. (R) is true.

Connection: While both are true, the reason for p ≤ 5 is the definition of the range of probability (0 ≤ P(E) ≤ 1), not specifically the formula for the complement event. 

Thus, (R) is not the explanation for (A).