Question

If the probability of an event occurring is 0.25, what is the probability that the event does not occur?

Answer 1

Step 1: Recall the rule of complementary probability.

The sum of the probabilities of an event occurring and not occurring is always 1. \[ P(\text{event}) + P(\text{not event}) = 1 \]

Step 2: Substitute the given probability.

Given \( P(\text{event}) = 0.25 \), \[ 0.25 + P(\text{not event}) = 1 \]

Step 3: Solve for \( P(\text{not event}) \).

\[ P(\text{not event}) = 1 - 0.25 = 0.75 \]

Final Answer: \(\boxed{0.75}\)

Short Explanation (Why this works)

Every event has a complement — it either happens or it doesn’t. The total probability of all possible outcomes equals 1, so the probability of the event *not occurring* is \( 1 - P(\text{event}) = 0.75 \).