Question

If \(P(E) = 0.02\) then \(P(E')\) is equal to

• A. 0.02
• B. 0.002
• C. 0.98
• D. 0.97

Hint:

An event and its complement cover all possible outcomes. Think of it as a percentage: if there is a 2% chance of something happening, there is a 98% (100% - 2%) chance of it not happening.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This question deals with complementary events in probability. \(E'\) (or \(\bar{E}\)) represents the complement of event E, meaning the event that E does not occur. The sum of the probabilities of an event and its complement is always 1.

Step 2: Key Formula or Approach:
The formula for the probability of a complementary event is:
\[ P(E') = 1 - P(E) \]

Step 3: Detailed Explanation:
We are given the probability of event E:
\[ P(E) = 0.02 \] Using the formula, we can find the probability of its complement, \(E'\):
\[ P(E') = 1 - 0.02 \] \[ P(E') = 0.98 \]

Step 4: Final Answer:
The value of \(P(E')\) is 0.98.