Puzzle #195: Chocolate

Your sweetie loves chocolate. You bought your sweetie some chocolate: an assortment of 24 chocolates with six each of four flavours. “Oh, honey, you shouldn’t have.” Why not? Unfortunately, chocolate causes your sweetie to gain weight per the following table:

Flavour Weight Gain in Grams per Chocolate Eaten

Nougat 100
Honey 200
Solid Chocolate 900
Anthrax Ripple -200

Your sweetie selects four chocolates at random and eats them.

What is the probability of each of the following scenarios occurring (assuming no other factors that affect weight)?

Scenario 1: Your sweetie gains two or more kilograms.

Scenario 2: Your sweetie’s weight does not change.

Scenario 3: Your sweetie loses weight.

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, March 1, 2017 at noon Pacific Time. I will post the answer shortly after.