A nancial manager made two new investmentsone in the oil industry and one in municipal bonds. After a one-year period, each of the investments will be classified as either successful or unsuccessful. Consider the making of the two investments as a random experiment. (a) How many sample points exist for this experiment? |:l sample pom (b) Construct a tree diagram for the experiment. (Let S : successful and U : unsuccessful.) Tree Diagram Description Oil Industry M unici pal Bonds List the sample points. (Select all that apply.) O(U, U, S) O(S) O(S, S) O(S, U, S) O(U, S, U) O(U, U) O(U, U, U) O(S, S, S) O(S, U) O(S, S, U) O(U) O(U, S) (c) Let O = the event that the oil industry investment is successful. List the sample points in O. (Select all that apply.) O(U, U, S) O(S) O(S, S) O(S, U, S) O(U, S, U) O(U, U) O(U, U, U ) O(S, S, S) O(S, U) O(S, S, U) O(U) O(U, S) Let M = the event that the municipal bond investment is successful. List the sample points in M. (Select all that apply.) O(U, U, S) O(S) O(S, S) O(S, U, S) O(U, S, U) O(U, U) O(U, U, U) O(S, S, S) O(S, U) O(S, S, U) O(U) O(U, S) (d) List the sample points in the union of the events (O U M). (Select all that apply.) O(U, U, S) O(S) O(S, S) O(S, U, S) O(U, S, U) O(U, U) O(U, U, U) O(S, S, S) O(S, U) O(S, S, U) O(U) O(U, S) (e) List the sample points in the intersection of the events (0 n M). (Select all that apply.) O(U, U, S) O(S) O(S, S) O(S, U, S) O(U, S, U) O(U, U) O(U, U, U) O(S, S, S) O(S, U) O(S, S, U) O(U) O(U, S) (f) Are events O and M mutually exclusive? Why or why not? O No, since O n M has a sample point. O Yes, since O n M has a sample point. O No, since O n M has no sample point. O Yes, since O n M has no sample point