Question

Let \( E' \) denote the complementary event of \( E \). If \( P(E) = \frac{1}{13} \), then \( P(E') \) is:

• A. \( \frac{12}{13} \)
• B. \( \frac{13}{12} \)
• C. \( \frac{1}{13} \)
• D. \( \frac{1}{12} \)

Hint:

The probability of the complementary event is simply \( 1 - P(E) \).

Answer 1

The Correct Option is A

Let’s break down the solution step by step: Step 1: The sum of probabilities of an event and its complementary event is 1. Therefore, \[ P(E') = 1 - P(E) = 1 - \frac{1}{13} = \frac{13}{13} - \frac{1}{13} = \frac{12}{13} \] Thus, the correct answer is \( \frac{12}{13} \).

Step 2: Conclusion: Since the probability of the complementary event is \( \frac{12}{13} \), the correct answer is (1) \( \frac{12}{13} \).