The conditional probability of Tom finding Jerry

My all time favourite catch is “JERRY catching TOM!” ?

Little Jerry is so smart, and do you know that he knows probability as well?

One day, Jerry was thinking, “Hmm, every time Tom chases me, I end up in one of three possible places: the mouse hole, the kitchen, or the garden. Let’s compute the conditional probability of Tom finding me in the kitchen, given that he has already looked in the mouse hole and didn’t find me.” Then, he started scribbling on the chalkboard:

1. Define Events:

• : Jerry is in the kitchen.
• : Tom looks in the mouse hole and doesn’t find Jerry.

1. Probabilities:

• (Since there are three equally likely places)
• (If Jerry is in the kitchen, there’s a 50% chance Tom checks the mouse hole first)
• (If Jerry is not in the kitchen, Tom definitely checks the mouse hole)

1. Use Bayes’ Theorem:
2. Compute :
3. Final Calculation:
   Then, Jerry smirked in a triumph manner upon looking at the results, “Aha! There’s only a 20% chance Tom will find me in the kitchen if he’s already checked the mouse hole!”

Very soon after Jerry left, Tom bursted in and looked around confusedly, eventually gave up and left.

Jerry relieved, “Works every time! Now, back to my cheese.”

Have you notice if Jerry compute any other probability problem? Comment below ?