I'm working on a capstone design project and am struggling to find some of the probabilities I need to formulate my model. We have a collection of data from a portion of my school's student body that we are trying to parse through based on year in school, what school they're in, and their gender. One survey question asked about knowledge of a particular campus resource, so our goal is to find the probability that a student knows about the resource given his/her year, gender and school (e.g. what is the probability that a student knows about the resource given that he is a freshman, male engineering student, or that she is a sophomore, female business student?).

We have exact data from the school on the number of people in each class, the number of people in each school, and the number of people of each gender. The responses to our survey were approximately spread according to the school's exact data (i.e. we received approximately the same percentage of freshmen-senior responses that the school actually has). However, when we broke it down based on school, gender and year, we did not have significant responses from each group (e.g. we only received 2 sophomore, male engineering student responses).

However, we were able to calculate the probabilities that a student knows about the resource for each broad group. That is, we have the probability that a female vs a male knows about the probability, the probability that an engineering student vs business student vs other schools knows about the resource, etc. Is there a way we can use the probabilities of each broad group to find the probabilities for each specific group?

Thank you in advance!