The next two problems utilize the information in the following paragraph.
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.
Then, what is the probability of being both Short-haired and working at a Small firm? (Need to know how to get bold answer with showing work)
a. .08 b. .14 c. .55 d. .72 e. .40
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 __.
a. .17 b. .25 c. .40 d. .54 e. .68