Question

Assertion (A) : The probability that the date of birth of a man is in the month of June is \(\frac{1}{12}\).
Reason (R) : There are 12 months in a year.

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

In probability questions involving calendars, we make the simplifying assumption that all months are equally likely, ignoring the slight variation in the number of days per month (28, 30, or 31).
Under this equal-likelihood assumption, the probability of selecting any specific month is always \(\frac{1}{12}\).

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
This is an Assertion-Reason question. We need to evaluate whether the Assertion is mathematically correct, whether the Reason is true, and if the Reason explains why the Assertion is true.

Step 2: Key Formula or Approach:
The probability of an event \(E\) is given by:
\[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \]
In this context, the outcomes represent the months of the year.

Step 3: Detailed Explanation:
1.

Evaluate Assertion (A):
We are considering the month in which a person is born.
Assuming that a birth is equally likely to occur in any month of the year:
The event \(E\) is "being born in June".
There is exactly 1 month called June. So, the number of favorable outcomes is 1.
If there are 12 months in a year, the total number of possible outcomes is 12.
Therefore, the probability of being born in June is:
\[ P(E) = \frac{1}{12} \]
Thus, Assertion (A) is true.

2.

Evaluate Reason (R):
The Reason states that "There are 12 months in a year".
This is a standard fact of the calendar. Therefore, Reason (R) is true.

3.

Determine if Reason (R) is the correct explanation for Assertion (A):
The reason the probability of being born in June is \(\frac{1}{12}\) is precisely because June is one specific month out of the total of 12 months that make up a year.
Therefore, the Reason directly provides the correct basis for the mathematical calculation in the Assertion.

Step 4: Final Answer:
Both Assertion and Reason are true, and the Reason is the correct explanation for the Assertion. This matches option (A).