Suppose 30% of the graduate students live in a dorm but only 10% of the undergraduate students live in a dorm. If a student smokes and lives in the dorm, is he or she more likely to be a graduate or undergraduate student? You can assume independence between students who live in a dorm and those who smoke.

What will be an ideal response?

First, we need to estimate all the probabilities.

P(D|UG)=0.1, P(D|G)=0.3.

P(D) = P(UG).P(D|UG)+P(G).P(D|G)=0.8?0.1+0.2?0.3=0.14.

P(S) = P(S|UG)P(UG)+P(S|G)P(G)=0.15?0.8+0.23?0.2=0.166.

P(DS|G) = P(D|G) × P(S|G)=0.3 × 0.23 = 0.069 (using conditional

independent assumption)

P(DS|UG) = P(D|UG) × P(S|UG)=0.1 × 0.15 = 0.015.

We need to compute P(G|DS) and P(UG|DS).