Katie,

(1) this is a conditional probability. Probability that event 2 will happen given that event 1 has happened.

case 1: Probability that the first ball is yellow = 5/12

Probability that the second ball is yellow given that the first ball is yellow is 5/12

=> Probability that the second ball is yellow = (Probability that the first ball is yellow)(Probability that the second ball is yellow given that the first ball is yellow) = (5/12)(5/12)

Case 2: Probability that the first ball is not yellow = 7/12

=> Probability that the second ball is yellow = (Probability that the first ball is yellow)(Probability that the second ball is yellow given that the first ball is yellow) = (5/12)(5/12)

Case 2: Probability that the first ball is not yellow = 7/12

Probability that the second ball is yellow given that the first ball is not yellow is 5/11

=> Probability that the second ball is yellow = (Probability that the first ball is not yellow)(Probability that the second ball is yellow given that the first ball is not yellow) = (7/12)(5/11)

Total probability = p1 + p2 = (5/12)(5/12) + (7/12)(5/11)

(2) pretty much the same applies for this but it way more involved: give 1st ball is/not yellow, given 1st ball is/not red.... I hope this helps.