A and B are chosen randomnly chosen from [0,1] in a independent and uniform way.

For part 1, 2, and 3 , briefly (1) graph the intersection of set of interest, (2) set on which the density function is nonzero and (3) calculate each probability.

Part 1: P(AB 0.5)

Part 2: P(|AB| 0.5)

Part 3: P(A² +B² 1)