Question 14
Professor Guilherme creates three strange machines. Machine $A$ turns a cat into a dog with probability $1/3$; machine $B$ does so with probability $2/5$; and machine $C$ with probability $1/4$. If the animal is a dog, none of the machines changes it.
He puts a cat into $A$, then the resulting animal into $B$, and finally the animal from $B$ into $C$. What is the probability that a dog comes out of $C$?
He puts a cat into $A$, then the resulting animal into $B$, and finally the animal from $B$ into $C$. What is the probability that a dog comes out of $C$?