Answer:
water is Arthur's favorite drink
Explanation:
The three drinks are lemonade, milk, and water.
If Paige's drink is a dairy product, milk would be the only answer there.
If Frank's drink comes from a fruit, lemonade would be the answer. Lemonade is made from lemons and sugar.
Water is the only choice left and Arthur is the only person who doesn't have a drink.
So, Arthur's favorite drink would be water.