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 is 57%, which can be expressed as:
\[P(E) = 57\% = 0.57\] where \(P(E)\) represents the probability of event \(E\).

Step 1: Complement Rule
The probability of an event *not* happening is the complement of the event. The sum of an event's probability and its complement always equals 1:
\[P(E) + P(E') = 1\] where \(P(E')\) is the probability of event \(E\) *not* happening.

Step 2: Calculate the Probability of the Event Not Happening
Using the complement rule:
\[P(E') = 1 - P(E)\] Substitute the given value:
\[P(E') = 1 - 0.57 = 0.43\]

Step 3: Interpretation
The probability the event does not happen is 0.43, equivalent to a 43% chance the event will not occur.

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