Solution:

For part (a), pick boxes containing 22 different candies chosen at random. Let their total cost be $m$ cents. If $m \leq 75$, Anna can buy these candies. Otherwise, $m \geq 76$. In this case, the other 22 candies have a total cost of $151-m \leq 75$ cents, so Anna can buy those candies instead.

For part (b), rank the candies from most to least expensive and consider the $19^{\text{th}}$ candy in the ranking. If this candy costs 4 cents or more, then the first 19 candies cost at least 76 cents and so the last 25 candies cost at most 75 cents. But if the $19^{\text{th}}$ most expensive candy costs 3 cents or less, then so do the remaining 25 candies in the list, so the last 25 candies again cost at most 75 cents.