To solve this problem, we can use the principle of inclusion-exclusion. Let's break it down step by step:

1. Total number of people surveyed: 900

2. Percentage of people with a cat: 31% $0.31 \times 900 = 279 \text{ people with a cat}$

3. Percentage of people with a bird: 34% $0.34 \times 900 = 306 \text{ people with a bird}$

4. Estimating the percentage of people who have both a cat and a bird: Assuming that the ownership of a cat and a bird are independent events, the percentage of people who have both pets is: 0.31 \times 0.34 = 0.1054 \text{ or 10.54%}

5. Calculating the number of people who have both pets: $0.1054 \times 900 = 94.86$

   Rounding to the nearest whole number gives us 95 people.

So, approximately 95 people have both a cat and a bird.

Would you like more details or have any questions about this? Here are some related questions:

1. How would the calculation change if the cat and bird ownership were not independent?
2. What is the probability that a person chosen at random has neither a cat nor a bird?
3. If 40% of the people with cats also have birds, how many people is that?
4. How many people have either a cat or a bird, but not both?
5. How would you calculate the expected overlap if the percentages were different?

Tip: Always check if events are independent before multiplying their probabilities.