Suppose there are two types of law school students: short haired and long haired. Additionally, law students generally choose between two types of firms when they graduate: big and small. Suppose the probability of being short haired is .8, and a short haired student will end up at a big firm 90% of the time.
1. What is the probability of being both short haired and working at a small firm?
2. Additionally, suppose the probability of working at a big firm is .75, then amongst the small firm students, the probability of being long haired is...?