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Suppose there is a recipe that calls for 3 tsp of cinnamon. Since people have strong feelings about this spice, it is common for people

Suppose there is a recipe that calls for 3 tsp of cinnamon. Since people have strong feelings about this spice, it is common for people to adjust the recipe after trying it. Suppose that no matter who uses the recipe or how much cinnamon it calls for, there is a 30% chance the user will increase the cinnamon by 1 tsp, a 50% chance they leave the cinnamon unchanged, and a 20% chance they decrease the cinnamon by 1 tsp. Also, assume people's adjustments are independent. Suppose person A uses the recipe and makes their alteration, and then passes their altered recipe to person B. What is the probability that after person B has made their alteration the recipe calls for the original amount of cinnamon, 3 tsp? (Here, the word "alteration" includes the possibility that a person will leave the cinnamon amount unchanged.) [WISE, VIZ]

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