[AaronBrown]

Jay_Shark is correct, but you have to be careful with this kind of question.

Your second calculation would be correct if the Celtics could win more than one pick. That is, if the NBA drew the balls and if the Celtics were on the first and second ball, they got both picks. This doesn't happen, of course, in that case the NBA throws out the second ball and picks again until they get a team other than Boston.

Another computation would be correct if you were given the probability of the Celtics winning the second pick, assuming they don't win the first. People often state probabilities this way (technically, that would be a "conditional" probability). In this case, the conditional probability is 23.5%. Then your calculation would be:

0.188 + (1 - 0.188)*0.235 = 0.387 (the same as adding 0.199 + 0.188).