We are asked to find the conditional probability that a graduate is currently working in nursing, given that they earned a bachelor's degree.

This conditional probability can be calculated using the formula:

$P(\text{in nursing} \mid \text{bachelor's}) = \frac{P(\text{in nursing and bachelor's})}{P(\text{bachelor's})}$

Given:

• $P(\text{bachelor's degree}) = 0.45$
• $P(\text{working in nursing and bachelor's}) = 0.40$

We can now substitute these values into the formula.

$P(\text{in nursing} \mid \text{bachelor's}) = \frac{0.40}{0.45}$

Let's calculate this.The probability that a graduate is currently working in nursing, given that they earned a bachelor's degree, is approximately $0.889$, or 88.9%.

Would you like further details or have any other questions?

Here are 5 related questions for further exploration:

1. What is the probability that a graduate has a bachelor's degree, given that they are working in nursing?
2. If a graduate does not have a bachelor's degree, what is the probability that they are working in nursing?
3. What is the probability that a graduate neither has a bachelor's degree nor is working in nursing?
4. How does the probability change if 60% of graduates have a bachelor's degree?
5. What is the joint probability that a graduate both has a bachelor's degree and is not working in nursing?

Tip: Conditional probability helps refine predictions by incorporating relevant known information, which makes it especially useful in decision-making scenarios.