statistical significance in probabilities

Question

Imagine I am conducting an experiment, and I record whether $n$ individuals of different nationalities, say $A$, $B$, and $C$, either like or dislike a product.

In the end I have the respective numbers, denote them $a$, $b$, and $c$, of people who like the product. How to compute whether the difference is significant?

My first approach would be to make a t-test in which the numerator is the difference between $a$ and $b$ divided by $n$, but I am not sure what the denominator should be. Since it measures the variability between groups should be the variance but note that the variance between 0s and 1s doesn't say much. (0 for unlike and 1 for like).

Or should I estimate a probit model including the nationalities as independent variables, and check whether they are significant for predicting the probability of liking the product?

Intuitive explanations and examples are most welcomed. Thanks,

Answer 1

A $\chi^2$ test would be appropriate since we are dealing with observed frequencies from mutually exclusive groups

Answer 2

If the $\chi^2$ test David suggested fails $H_0$ , i.e., that all means are equal, you can then use, either Fisher's LSD test or, for non-parametric, you can use Kruskal-Wallis , to decide which two ( or more ) means are not equal ( at the given choice of significance).