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March Randomness #10

Pouch A has two blue balls and one red ball. Pouch B has three blue balls. Pouch C has three red balls. Without looking, take two balls from Pouch A and put them in Pouch B. Shuffle Pouch B and without looking, take two balls from Pouch B and put them into Pouch C. Finally, shuffle Pouch C and without looking take one ball from Pouch C. Will it be red?

Intuition

Simulation

Calculation