March Randomness #10

[size=200]Pouch A has two blue balls and one red ball.[br]Pouch B has three blue balls.[br]Pouch C has three red balls.[br][br]Without looking, take two balls from Pouch A and put them in Pouch B.[br][br]Shuffle Pouch B and without looking, take two balls from Pouch B and put them into Pouch C.[br][br]Finally, shuffle Pouch C and without looking take one ball from Pouch C.[br][br]Will it be red?[/size]
Intuition
Simulation
Calculation

Information: March Randomness #10