three members of a private country club have been nominated for the office of president. The probability that Mr. Adams will be elected is 0.3. The probability that Mr. Brown will be elected is 0.5. The probability that Ms. Cooper will be elected is 0.2. Should Mr. Adams be elected, the probability of an increase in membership fees is 0.8. Should Mr. Brown or Ms. Cooper be elected, the corresponding probabilities for an increase in fees are 0.1 and 0.4.

a) What is the probability that there will be an increase in membership fees?

b)

If it is known that membership fees have increased, what is the probability that Ms. Cooper was elected?