Mathematics
Mathematics
Problem
The probability that a particular salesman will leave his sunglasses behind in any store is . Suppose the salesman visits two stores in succession and leaves his sunglasses behind in one of them. What is the probability that the salesman left his sunglasses in the first store?Intuitive explanation
This is a conditional probability problem where you need to find the probability of a specific event given that you already know something happened. The key insight is to use Bayes' theorem: figure out all the ways the salesman could leave his sunglasses in exactly one store, then calculate what fraction of those scenarios involve the first store. You're not looking for the probability he leaves them in store 1 overall—you're restricting to the world where he left them in exactly one store, then asking what portion of that world is store 1.
Intuitive explanation
This is a conditional probability problem where you need to find the probability of a specific event given that you already know something happened. The key insight is to use Bayes' theorem: figure out all the ways the salesman could leave his sunglasses in exactly one store, then calculate what fraction of those scenarios involve the first store. You're not looking for the probability he leaves them in store 1 overall—you're restricting to the world where he left them in exactly one store, then asking what portion of that world is store 1.