Assertion : A die is thrown. Let E be the event that number appears on the upper face is less than 1, then P( E) = `1/6`
Reason : Probability of impossible event is 0.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are tme but reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If assertion is false but reason is true.

Answer

To solve the problem, we need to analyze both the assertion and the reason provided.

### Step 1: Understand the Assertion
The assertion states that when a die is thrown, the event \( E \) is defined as the number appearing on the upper face being less than 1. We need to find the probability \( P(E) \).

### Step 2: Identify the Sample Space
When a die is thrown, the possible outcomes (sample space) are:
\[ S = \{1, 2, 3, 4, 5, 6\} \]
This means there are a total of 6 outcomes.

### Step 3: Determine the Favorable Outcomes for Event \( E \)
The event \( E \) states that the number on the upper face is less than 1. However, the smallest number on a die is 1. Therefore, there are no outcomes in the sample space that satisfy this condition. Thus, the number of favorable outcomes for event \( E \) is:
\[ \text{Favorable outcomes} = 0 \]

### Step 4: Calculate the Probability of Event \( E \)
The probability of an event is calculated using the formula:
\[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
Substituting the values we found:
\[ P(E) = \frac{0}{6} = 0 \]

### Step 5: Evaluate the Assertion
The assertion claims that \( P(E) = \frac{1}{6} \). However, we calculated \( P(E) = 0 \). Therefore, the assertion is **false**.

### Step 6: Understand the Reason
The reason states that the probability of an impossible event is 0. An impossible event is defined as an event that cannot occur. Since event \( E \) (the number on the die being less than 1) is indeed impossible, its probability is 0. Therefore, this statement is **true**.

### Conclusion
- The assertion is **false**.
- The reason is **true**.

Thus, the correct answer is that the assertion is false, and the reason is true.

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