3.98 Staff, Inc., a management consulting company, is surveying the personnel of Acme Ltd. It determined that 35% of the analysts have an MBA and that 40% of all analysts are over age 35. Further, of those who have an MBA, 30% are over age 35.

a. What is the probability that a randomly chosen analyst both has an MBA and also is over age 35?

b. What is the probability that a randomly chosen analyst who is over age 35 has an MBA?

c. What is the probability that a randomly chosen analyst has an MBA or is over age 35?

d. What is the probability that a randomly chosen analyst who is over age 35 does not have an MBA?

e. Are the events MBA and over age 35 independent?

f. Are the events MBA and over age 35 mutually exclusive?
g. Are the events MBA and over age 35 collectively exhaustive?