In a certain population, 10% of the people are rich, 5% are famous, and 3% are rich and famous. Then find the probability that a person picked at random from the population is either famous or rich but not both.

Explanation

To solve the problem, we need to find the probability that a person picked at random from the population is either famous or rich, but not both. We can break this down step by step.

### Step 1: Define the Events
Let:
- \( R \) = event that a person is rich
- \( F \) = event that a person is famous

From the problem, we know:
- \( P(R) = 0.10 \) (10% are rich)
- \( P(F) = 0.05 \) (5% are famous)
- \( P(R \cap F) = 0.03 \) (3% are both rich and famous)

### Step 2: Calculate the Probability of Being Rich but Not Famous
The probability that a person is rich but not famous can be expressed as:
\[ P(R \cap F') = P(R) - P(R \cap F) \]
Substituting the known values:
\[ P(R \cap F') = 0.10 - 0.03 = 0.07 \]

### Step 3: Calculate the Probability of Being Famous but Not Rich
The probability that a person is famous but not rich can be expressed as:
\[ P(F \cap R') = P(F) - P(R \cap F) \]
Substituting the known values:
\[ P(F \cap R') = 0.05 - 0.03 = 0.02 \]

### Step 4: Calculate the Total Probability of Being Either Famous or Rich but Not Both
Now, we need to find the total probability that a person is either famous or rich but not both. This can be calculated by adding the probabilities from Steps 2 and 3:
\[ P(R \cap F') + P(F \cap R') = 0.07 + 0.02 = 0.09 \]

### Conclusion
Thus, the probability that a person picked at random from the population is either famous or rich but not both is:
\[ \boxed{0.09} \]