Pregunta
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In a loan database, there are 27 loans to clients with 8 years of business experience. Also,
there are 29 loans made to clients with a Graduate education. In the database there are 52
loans to clients with 8 years of experience or who have a Graduate education. How many
loans were made to clients with a Graduate education who also had 8 years of experience?
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Ask by Stanley Ball. in the United States
Mar 22,2025

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There are 4 loans to clients with both a Graduate education and 8 years of experience.

Solución

We start with the formula for the union of two sets:
where:
  • (loans with 8 years of experience),
  • (loans to clients with a Graduate education),
  • (loans to clients with 8 years of experience or a Graduate education).
Substituting the given values:
Simplify the sum:
Solve for by subtracting 52 from 56:
Thus, the number of loans to clients with both a Graduate education and 8 years of experience is:

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The Deep Dive

To find the number of loans made to clients with both 8 years of experience and a Graduate education, we can use the principle of inclusion-exclusion.
Let:
  • be the loans to clients with 8 years of experience = 27
  • be the loans to clients with Graduate education = 29
  • be the loans to clients with either 8 years of experience or a Graduate education = 52
Using the formula:
Where is the number of loans made to clients who fall into both categories.
Plugging in our values:
Thus, the number of loans made to clients with a Graduate education who also had 8 years of experience is .

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