In a model where y is qualitative, our objective is to estimate its expected or mean value given the value of the regressors True or false

True.

When y is a qualitative variable (e.g., binary like 0 or 1, or categorical), the objective of models like logit or probit is to estimate the probability of a particular outcome occurring given the regressors. For a binary qualitative variable coded as 0 or 1, the expected value E[y|x] is precisely the probability P(y=1|x). Therefore, estimating the expected value of a qualitative dependent variable is equivalent to estimating the probability of the outcome.