We are asked to find $P(B \mid A)$, the conditional probability of $B$ given $A$.

The formula for conditional probability is:

$P(B \mid A) = \frac{P(A \text{ and } B)}{P(A)}$

From the given dataWe are asked to find $P(B \mid A)$, the conditional probability of $B$ given $A$.

The formula for conditional probability is:

$P(B \mid A) = \frac{P(A \text{ and } B)}{P(A)}$

From the given

• $P(A) = 0.34$
• $P(A \text{ and } B) = 0.05$

Now, we can substitute these values into the formula:

$P(B \mid A) = \frac{0.05}{0.34}$

Let me calculate that.The conditional probability $P(B \mid A)$ is approximately $0.1471$ when rounded to four decimal places.

Would you like further details or have any questions? Here are five related questions to deepen understanding:

1. How would you calculate $P(A \mid B)$ given the same data?
2. What does it mean if $P(B \mid A)$ is close to 1 or 0?
3. How can we verify if events $A$ and $B$ are independent based on their probabilities?
4. What is the complement rule for conditional probabilities?
5. How would this change if the events $A$ and $B$ were mutually exclusive?

Tip: The conditional probability $P(B \mid A)$ shows the likelihood of $B$ occurring given that $A$ has already happened. It can be useful in many real-world decision-making scenarios!