Questions: If the P(A)=0.09, what is the probability that event A does not occur?

Transcript text: If the $P(A)=0.09$, what is the probability that event $A$ does not occur?

Solution

Solution Steps

Step 1: Understanding the Problem

We are given the probability of an event $ A $ occurring, denoted as $ P(A) = 0.09 $. We need to find the probability that event $ A $ does not occur.

Step 2: Using the Complement Rule

The probability that event $ A $ does not occur is the complement of the probability that event $ A $ does occur. The complement rule in probability states that:

\[ P(A') = 1 - P(A) \]

where $ P(A') $ is the probability that event $ A $ does not occur.

Step 3: Calculating the Complement Probability

Substitute the given probability $ P(A) = 0.09 $ into the complement rule formula:

\[ P(A') = 1 - 0.09 = 0.91 \]