**b.** The probability that a randomly selected small business owner has a business relationship with a bank or credit union or is Latino is

To find the probability that a randomly selected small business owner either has a business relationship with a bank or credit union or is Latino, we can use the concept of the union of two events in probability.

### Step 1: Define the Events
- Let \( A \) be the event that a small business owner has a business relationship with a bank or credit union.
- Let \( B \) be the event that a small business owner is Latino.

### Step 2: Data Interpretation
From the given dataTo find the probability that a randomly selected small business owner either has a business relationship with a bank or credit union or is Latino, we can use the concept of the union of two events in probability.

### Step 1: Define the Events
- Let \( A \) be the event that a small business owner has a business relationship with a bank or credit union.
- Let \( B \) be the event that a small business owner is Latino.

### Step 2: Data Interpretation
From the given 

- The total number of small business owners surveyed, \( n = 131 \).
- The number of small business owners with a business relationship, \( |A| = 91 \).
- The number of Latino small business owners, \( |B| = 52 \).
- The number of Latino small business owners who have a business relationship, \( |A \cap B| = 35 \).

### Step 3: Use the Formula for Union of Two Events
The probability of the union of two events \( A \) and \( B \) is given by:

\[
P(A \cup B) = P(A) + P(B) - P(A \cap B)
\]

where:
- \( P(A) \) is the probability that a randomly selected small business owner has a business relationship with a bank or credit union.
- \( P(B) \) is the probability that a randomly selected small business owner is Latino.
- \( P(A \cap B) \) is the probability that a randomly selected small business owner both has a business relationship and is Latino.

### Step 4: Calculate Individual Probabilities
1. **Probability of having a business relationship** (\( P(A) \)):

   \[
   P(A) = \frac{|A|}{n} = \frac{91}{131}
   \]

2. **Probability of being Latino** (\( P(B) \)):

   \[
   P(B) = \frac{|B|}{n} = \frac{52}{131}
   \]

3. **Probability of both having a business relationship and being Latino** (\( P(A \cap B) \)):

   \[
   P(A \cap B) = \frac{|A \cap B|}{n} = \frac{35}{131}
   \]

### Step 5: Plug Values into the Formula

\[
P(A \cup B) = \frac{91}{131} + \frac{52}{131} - \frac{35}{131}
\]

\[
P(A \cup B) = \frac{91 + 52 - 35}{131}
\]

\[
P(A \cup B) = \frac{108}{131}
\]

### Step 6: Calculate the Probability

\[
P(A \cup B) \approx 0.8244
\]

Thus, the probability that a randomly selected small business owner has a business relationship with a bank or credit union or is Latino is approximately **0.8244**.

Would you like further details or have any questions? Here are some related questions to consider:

1. What is the probability that a randomly selected Latino small business owner does not have a business relationship with a bank or credit union?
2. How would you find the probability that a small business owner is either Black or has a business relationship with a bank or credit union?
3. What is the probability that a randomly selected business owner is neither Latino nor has a business relationship?
4. How does the concept of mutually exclusive events affect the calculation of probabilities for different groups?
5. How would the probability change if the number of Latino business owners with a relationship changed?

**Tip:** When using the union formula \( P(A \cup B) = P(A) + P(B) - P(A \cap B) \), always remember to subtract the intersection \( P(A \cap B) \) to avoid double-counting.

Learn how to calculate the probability that a randomly selected small business owner either has a business relationship with a bank or credit union or is Latino using probability theory. Includes step-by-step calculation with data interpretation and formula application.

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