Question

If E and E are the events of occurrence and non-occurrence of a random experiment respectively and P(E) = 0-05, then P(E) =

• A. 0-05
• B. 0.5
• C. 0.9
• D. 0.95

Answer 1

The Correct Option is D

We are tasked with finding \( P(\overline{E}) \), the probability of the non-occurrence of an event \( E \), given that \( P(E) = 0.05 \).

Step 1: Use the complement rule.

The sum of the probabilities of an event and its complement is always 1:

\[ P(E) + P(\overline{E}) = 1. \]

Step 2: Substitute \( P(E) = 0.05 \) into the equation.

\[ 0.05 + P(\overline{E}) = 1. \]

Step 3: Solve for \( P(\overline{E}) \).

\[ P(\overline{E}) = 1 - 0.05 = 0.95. \]

Final Answer: The probability of the non-occurrence of the event is \( \mathbf{0.95} \), which corresponds to option \( \mathbf{(4)} \).