Question

Assertion (A): The probability of selecting a number at random from the numbers 1 to 20 is 1. Reason (R): For any event E, if P(E) = 1, then E is called a sure event.

• A. Both A and R are true, and R is the correct reason for A.
• B. Both A and R are true, and R is not the correct reason for A.
• C. A is true, but R is false.
• D. A is false, but R is true

Answer 1

Answer: (B)

Option b. Both A and R are true, and R is not the correct reason for A.

Answer 2

Solution:

1. Assertion (A): When selecting a number from the set {1, 2, …, 20}, the outcome is always one of these numbers. Hence, the event “a number is selected” is certain and its probability is 1.

2. Reason (R): By definition, if $P(E) = 1$ for some event $E$, then $E$ is called a sure event. This is a standard definition in probability.

3. Analysis:

   • Both the assertion and the reason are true.
   • However, the reason only states the definition of a sure event and does not explain why the specific event in (A) (selecting a number from 1 to 20) necessarily has a probability of 1, which is due to the construction of the sample space.

Thus, both A and R are true, but R is not the correct reason for A.