A box contains only red chips, white chips, and blue chips.

The concept of mutually exclusive and exhaustive events helps us understand which methodology to use in which question.
Two events are mutually exclusive when they cannot both happen at the same time. e.g. picking a white chip and picking a blue chip are mutually exclusive events. If you pick out one chip, it will be either white or blue but not both.

When 2 or more events represent all possible events, they are called exhaustive events. Picking a white chip, picking a blue chip and picking a red chip are mutually exclusive and exhaustive events. When you pick out a chip, it has to be either blue or white or red. It cannot be a fourth color. Hence these 3 events represent all possible events that can take place. The sum of their probabilities will be 1. This is so because one of them HAS to take place.

In this question, when we know that probability of a red chip is 1/3, what is the remaining 2/3 probability? It is the probability that we will get either a white chip or a blue chip. Hence statement 2 is sufficient.

On the other hand, statement 1 just gives you the probability of blue chip as 1/5. This means 1/5th of the chips are blue but you do not know the probability of getting a white chip. So you do not know the probability of getting a white or a blue chip. If we had both P(blue) and P(white), we would have calculated it as:
P(blue or white) = P(blue) + P(white)