A financial manager made two new investments-one 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? sample points (b) Construct a tree diagram for the experiment. (Let S = successful and U = unsuccessful.) Tree Diagram Description Oil Industry | Municipal Bonds S ? v ? ? v List the sample points. (Select all that apply.) O( U) O(S, S, S) O(S, S, U) O( U, U, U ) O(S, U, S) O(S) O(U, S, U) D(U, U, S) O(S, S) O(U, S) O ( U, U ) O(S, U)(b) Construct a tree diagram for the experiment. (Let S = successful and U = unsuccessful.) Tree Diagram Description A tree diagram begins at a point and an upper and lower branch extend from this point to the right. From each of these two branches two more upper and lower branches extend to the right. The branches extending from the first point are displayed in a section labeled Oil Industry. These branches from top to bottom are labeled ? and U. The next set of branches are displayed in a section labeled Municipal Bonds. These branches from top to bottom are labeled S, ?, ?, and U. List the sample points. (Select all that apply.) O(U) O(s, S, S) O(S, S, U) O ( U, U, U ) O(S, U, S) D(S) O(U, S, U) O(U, U, S) O(S, S) O ( U, S ) O ( U, U ) O(S, U) (c) Let O = the event that the oil industry investment is successful. List the sample points in O. (Select all that apply.) O(U) O(S, S, S) O(S, S, U) O(U, U, U) O(S, U, S) D(S) O(U, S, U) O( U, U, S) O(S, S) O(U, S) ( U, U) O(S, U) Let M = the event that the municipal bond investment is successful. List the sample points in M. (Select all that apply.) O(U) O(s, S, S) O(S, S, U) O ( U, U, U ) O(S, U, S) O(S) O( U, S, U) O( U, U, S) O(S, S) D ( U, S ) O( U, U) O(S, U) (d) List the sample points in the union of the events (O U M). (Select all that apply.) O(U) O(S, S, S) O(S, S, U) O( U, U, U) O(S, U, S) O(S) O(U, S, U) O( U, U, S) O(S, S) O ( U, S ) O ( U, U ) O(S, U) (e) List the sample points in the intersection of the events (0 n M). (Select all that apply.) O(U) O(S, S, S) O(S, S, U) O( U, U, U) O(S, U, S) O(S) (U, S, U) O(U, U, S) O(S, S) D(U, S) O( U, U) O(S, U) (f) Are events O and M mutually exclusive? Why or why not? O Yes, since O n M has no sample point. O Yes, since O n M has a sample point. O No, since O n M has no sample point. O No, since On M has a sample point