# Can I use logistic regression if one category of the dependent variable has a very low frequency?

An example of 100 subjects. Let's say I wish to study the impact of literacy levels (0 as limited and 1 as adequate), anxiety levels (0 as no anxiety and 1 as severe anxiety) and sex (0 for female and 1 for male) on the decision that has been made.

We have decision A and decision B.

the frequency of decision A is 98 and the frequency of decision B is 2.

In such as scenario, is it reasonable to use logistic regression where the dependent variable is the binary variable (decision) ? Why/why not ?

A rule of thumb is to have $$10$$-$$15$$ members of the minority class per feature included in your regression. In your case, you have two such members, meaning that even one feature is too many to include.
Imbalance isn't really a problem, but a low number of minority-class observations might be. This is to say that $$98000$$ and $$2000$$ might not be so problematic but $$98$$ and $$2$$ probably is.
Unless you get more data, I do not see much hope for saying anything other than there being a $$2\%$$ chance of decision $$\text{B}$$, perhaps with a confidence interval.