Question 5 Use the following probabilities to answer the question. It may be helpful to sketch a Venn diagram. \( P(A)=0.5, P(B)=0.4 \) and \( P(A \) and \( B)=0.10 \). \( P( \) not \( B \mid A)=\square \) Round to 4 decimals. Question Help: Video \( \square \) Message instructor

To find \( P(\text{not } B \mid A) \), we can utilize the concept of conditional probability. This can be calculated as \( P(\text{not } B \mid A) = 1 - P(B \mid A) \). To find \( P(B \mid A) \), we use the formula \( P(B \mid A) = \frac{P(A \text{ and } B)}{P(A)} \). Thus, \( P(B \mid A) = \frac{0.10}{0.5} = 0.2 \). Therefore, \( P(\text{not } B \mid A) = 1 - 0.2 = 0.8 \). So, the final answer is \( 0.8000 \). Now, if you were to sketch a Venn diagram with two overlapping circles for events A and B, it would visually display the probabilities: A representing 50%, B overlapping A at the 10% for both A and B, and showcasing the remaining parts distinctly where neither occurs. It’s a fantastic way to visualize relationships and probabilities between multiple events, making it easier to grasp complex statistics!