There's a minigame in Mario Party 4 called "Hide and Go Boom". 4 players must compete in the game. There are 4 cannons labeled A,B,X, & Y. 3 players are "hiders", and 1 player the "seeker".
The Seeker has 3 attempts to catch everyone via lighting a fuse for one of the aforementioned cannons. (They choose 3 cannons to fire out of the 4)
What's the probability of this being the best choice from a hider's perspective, keeping in mind the following information; -The Seeker has three attempts and the cannon they select is eliminated once it has been shot -Hiders are not allowed to pick a new cannon or switch once they seeker begins lighting fuses -Hiders are able to be in any combination of cannons- see below scenarios
Scenario A (everybody takes their owns cannons): A, B, X are used, Y is empty. Scenario B (everyone jumps into one cannon) A is only used, all others remain empty Scenario C (2 in 1, and 1 in the other)
I've taken up to differential equations but not a single probability class in my life, so I'm struggling as how to model the probability for each scenario, notably scenario C.