The night of The Yule Ball was one of the most fun nights Hogwarts had seen in a long time. There was dance, music, food and what not. Luna Lovegood also had a pumpkin juice stall of her own which was quite a hit that night. She had brought 12 cartons of pumpkin juice for her stall and it finished in no time. At last only two of the bottles were left. Crab, Goyle and Harry, Ron approached the stall to buy 2 pumpkin juice bottles unaware of the fact that only two bottles were left.
As they reached the stall at the same time, Luna decided to give both the parties a fair chance of earning the pumpkin juice bottles.
She arranged 12 cartons in 3 x 4 grid and labelled them as A,B,C….L.
She has randomly chosen two of the cartons and hidden pumpkin juice bottles inside each of them, leaving the remaining ten cartons empty. She gives the dozen cartons to Crab, who opens them in the order A, B, C, D, E, F, G, H, I, J, K, L until he finds one of the bottles, whereupon he stops. The number of cartons that he opens is his score. Luna then reseals the cartons, keeping the bottles where they are, and presents the cartons to Ron, who opens the cartons in the order A, E, I, B, F, J, C, G, K, D, H, L, again stopping as soon as one of the bottles is found, and scoring the number of opened cartons. Whoever scores lower wins the game, if they score the same then it's a tie. For example, suppose Luna hides the bottles in cartons H and K. Then Crab will stop after reaching the bottle in carton H and will score 8, while Ron will stop after reaching the bottle in carton K and will score 9. So Crab wins in this case. Who is more likely to win this game?
(a) Ron
(b) Crab
(c) Both are equally likely to win
