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March Randomness #8

Pouch A has one blue ball and three red balls.  Pouch B has four blue balls. Pouch C has four 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 in Pouch C. Shuffle Pouch C and without looking, take two balls from Pouch C. Will they both be red?

Intuition

Simulation

Calculation