8. Solution. Let the correct numbers in the table be $a, b, c$ and $d$. Consider the events

$$
A=\{\text { There is a cat }\} \text { and } B=\{\text { There is a dog }\} .
$$

|  | There is a dog | There is no dog |
| :--- | :---: | :---: |
| There is a cat | $a$ | $b$ |
| There is no cat | $c$ | $d$ |

These events are independent if the proportion of "cat owners" among "dog owners" is the same as among "non-dog owners," i.e., the conditional probability of event $A$ given $B$ is equal to the probability of event $A$ given $\bar{B}: \mathrm{P}(A \mid B)=\mathrm{P}(A \mid \bar{B})$. We get ${ }^{1} \frac{a}{a+c}=\frac{b}{b+d}$, from which $a d=b c$.

Due to random variability in the data, this equality may not be exact, but it should hold at least approximately. Suppose that all numbers in the Scientist's report are correct except for $a$. Then $a$ is approximately (rounded to the nearest integer) $\frac{b c}{d}=\frac{1110 \cdot 978}{121} \approx 8972$, and the total number of respondents is approximately $8972+1110+978+121=11181$. This is much greater than the number of residents in the city, so this scenario is implausible.

Suppose now that the number $b$ is incorrect. In this case, $b \approx \frac{a d}{c}=\frac{765 \cdot 121}{978} \approx 95$, and the total number of respondents is approximately $765+95+978+121=1959$, which is much less than 3000. Similarly, if the number $c$ is incorrect, then $c \approx \frac{a d}{b}=\frac{765 \cdot 121}{1110} \approx 83$, and the total number of respondents is close to $765+1110+83+121=2079$, which is also too small.

If the incorrect number is $d$, then $d \approx \frac{b c}{a}=\frac{1110 \cdot 978}{765} \approx 1419$, and the total number of survey participants is approximately $765+1110+978+1419=4272$. This is possible.
Answer: approximately 4272 people.

Note. Instead of approximate equalities, estimates can be made using inequalities.

## Grading Criteria

| Solution is complete and correct | 2 points |
| :--- | :--- |
| Answer is correct, but there are no arguments showing that other options are implausible (for example, there is a guess about which number is incorrect) | 1 point |
| Solution is incorrect or missing | 0 points |