We are tasked with finding the conditional probability that a randomly chosen applicant has over 5 years of experience, given that the applicant has a graduate degree. This is a classic conditional probability problem.

The formula for conditional probability is:

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

Where:

• $A$ is the event "the applicant has over 5 years of experience."
• $B$ is the event "the applicant has a graduate degree."
• $A \cap B$ is the event "the applicant has both over 5 years of experience and a graduate degree."

From the problem, we have the following information:

• The total number of applicants is 445.
• 228 applicants have over 5 years of experience ($P(A) = \frac{228}{445}$).
• 103 applicants have both over 5 years of experience and a graduate degree ($P(A \cap B) = \frac{103}{445}$).
• 141 applicants have a graduate degree ($P(B) = \frac{141}{445}$).

Now, applying the formula:

$P(A \mid B) = \frac{P(A \cap B)}{P(B)} = \frac{\frac{103}{445}}{\frac{141}{445}} = \frac{103}{141}$

Thus, the probability that a randomly chosen applicant has over 5 years of experience, given that the applicant has a graduate degree, is:

$\frac{103}{141} \approx 0.7305$

So the answer is approximately 0.7305 or $\frac{103}{141}$.

Would you like more details on this solution, or do you have any questions?

Here are five related questions to explore further:

1. What is the probability that a randomly chosen applicant has a graduate degree?
2. What is the probability that a randomly chosen applicant has over 5 years of experience and no graduate degree?
3. What is the probability that a randomly chosen applicant has less than 5 years of experience?
4. How do you interpret conditional probabilities in real-world situations?
5. How does the total number of applicants affect the calculation of these probabilities?

Tip: When solving probability problems, always clearly define the events and ensure the conditions are well-understood. This will help avoid confusion between events and their intersections.