Out of 445
 applicants for a job, 228
 have over 5
 years of experience and 103
 have over 5
 years of experience and have a graduate degree.
Step 2 of 2 :  Consider that 141
 of the applicants have graduate degrees. What is the probability that a randomly chosen applicant has over 5
 years of experience, given that the applicant has a graduate degree? Enter a fraction or round your answer to 4
 decimal places, if necessary.

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.

Out of 445 applicants for a job, 228 have over 5 years of experience and 103 have over 5 years of experience and have a graduate degree. Consider that 141 of the applicants have graduate degrees. What is the probability that a randomly chosen applicant has over 5 years of experience, given that the applicant has a graduate degree? Enter a fraction or round your answer to 4 decimal places, if necessary.

Calculate the probability that a randomly chosen applicant has over 5 years of experience given they have a graduate degree, based on data from 445 applicants. This problem explores conditional probability using key formulas, suitable for students in Grades 10-12.

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