Questions: If P(A)=0.72, P(B)=0.11, and A and B are independent, find P(A B). A. 0.72 B. 0.83 C. 0.11 D. 0.0792

Transcript text: If $P(A)=0.72, P(B)=0.11$, and $A$ and $B$ are independent, find $P(A \mid B)$. A. 0.72 B. 0.83 C. 0.11 D. 0.0792

Solution

Solution Steps

To find $ P(A \mid B) $ when events $ A $ and $ B $ are independent, we use the property that for independent events, $ P(A \mid B) = P(A) $. This is because the occurrence of $ B $ does not affect the probability of $ A $.

Step 1: Given Information

We are given the probabilities $ P(A) = 0.72 $ and $ P(B) = 0.11 $. Additionally, it is stated that events $ A $ and $ B $ are independent.

Step 2: Applying the Independence Property

For independent events, the conditional probability $ P(A \mid B) $ can be expressed as: \[ P(A \mid B) = P(A) \] This means that the occurrence of event $ B $ does not affect the probability of event $ A $.

Step 3: Calculating $ P(A \mid B) $

Since $ P(A) = 0.72 $, we have: \[ P(A \mid B) = 0.72 \]