Question

Consider four multi-valued random variables C (campus), G (grade), M (major), and Y (year). We know that none of these variables are independent. We are provided the probability tables for the following joint, marginal, and conditional probabilities. P(Y) P(M) P(G,Y) P(C|Y) P(C,M) P(Y|M) For example, we are told: P(M=compSci) = 0.3, P(M=psych) = 0.2, P(M=bio)=0.2, P(M=business)=0.1P(G=A,Y=freshman)=0.03, P(G=B,Y=freshman)=0.12 , ... P(G=F , Y=senior)=0.08[corrected Jan 18, 11am] We are not provided any other probability tables; for example, we are not given values for: P(G=B) or P(M=psych, Y=junior) Explain how to combine probabilities from above to compute each probability below, or write“not possible” if it is not possible. For example: P(Y) = ∑? ?(?, ? = ?)

a) P（Y=freshman | C =RH）

Answer 1