Question

If probability of happening of an event is 57%, then probability of non-happening of the event is

• A. 0.43
• B. 0.57
• C. 53%
• D. \( \frac{1}{57} \)

Answer 1

The Correct Option is A

Given:
The probability of an event happening is given as 57%, which can be written as:
\[ P(E) = 57\% = 0.57 \] where \(P(E)\) denotes the probability of the event \(E\) occurring.

Step 1: Understanding the complement rule in probability
The probability of an event not happening is the complement of the event happening.
Mathematically, the sum of the probabilities of an event and its complement is always 1:
\[ P(E) + P(E') = 1 \] where \(P(E')\) is the probability of the event \(E\) not happening.

Step 2: Calculate the probability of the event not happening
Using the complement rule, we find:
\[ P(E') = 1 - P(E) \] Substitute the given value:
\[ P(E') = 1 - 0.57 = 0.43 \]

Step 3: Interpretation of result
The probability that the event does not happen is 0.43, which means there is a 43% chance that the event will not occur.

Final Answer:
\[ \boxed{ P(\text{event does not happen}) = 0.43 } \]