The nursing department of a college surveyed two hundred graduates from their programs about their current work. The college has different levels of degrees in nursing available. The department found the following probabilities:

\[\begin{aligned}
&P(\text{bachelor's degree})=0.45
\\\\
&P(\text{working in nursing})=0.85
\\\\
&P(\text{in nursing and bachelor's})=0.4
\end{aligned}\]

**Find the probability that a graduate is currently working in nursing, given that they earned a bachelor's degree.**

\[P\left( \text{in nursing }| \text{ bachelor's} \right)=\] 


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.

Learn how to calculate conditional probability for nursing graduates based on survey data. Find the probability that a graduate is currently working in nursing, given that they earned a bachelor's degree. Explore the application of conditional probability in real-world scenarios.

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