Of you looked at it say under a microscope, you would see the individual specks of red dye. There is dye in the drink mix obviously, but the other stuff like sugar, flavor, etc. all dissolves clear so you don’t see it, but it’s likely white and makes up more of the mix than the red dye. Depending on the size of the dye specks compared to the other bits, they may just be coated in smaller pieces of sugar for example or smaller than the sugar so is even harder see.
Powdered things look white because it means there are tons of tiny particles with surfaces at random angles where light diffracts creating diffuse reflection. The reason it’s white and not colored is likely the result of the powder being largely colorless substances like sugar with only a minor part of pigment but once everything is dissolved in water there are no longer diffracting surfaces only the pigment causing the water to turn red.
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