3.14 A fund manager is considering investing in a new software firm based in India. The manager’s assessment of probabilities for rates of return on this stock over the next year is summarized in the accompanying table. Let A be the event “rate of return will be at least 10%” and B be the event “rate of return will be negative.”

Rate of return Less than

–10%

–10%

to 6 0%

0% to 6 10%

10% to 6 20%

20% or more Probability 0.04 0.14 0.28 0.33 0.21

a. Find the probability of event A.

b. Find the probability of event B.

c. Describe the event that is the complement of A.

d. Find the probability of the complement of A.

e. Describe the event that is the intersection of A and B.

f. Find the probability of the intersection of A and B.

g. Describe the event that is the union of A and B.

h. Find the probability of the union of A and B.

i. Are A and B mutually exclusive?

j. Are A and B collectively exhaustive?