Question

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 making the two new investments as an experiment with the following four experimental outcomes Experimental Outcomes E1 E2 E3 E4 Oil Industry Successful Successful Unsuccessful Unsuccessful Municipal Bond Successful Unsuccessful Successful Unsuccessful a. How many sample points exist for this experiment? b. Choose a tree diagram.

Answer 1

a. The possible outcomes of this event are - { E₁ , E₂ ,  E₃ , E₄ }

Hence the number of sample points are 4.

b. We see in the given question -

	Oil	Municipal Bond
E1	Successful	Succesful
E2	Succesful	Unsuccessful
E3	Unsuccessful	Succesful
E4	Unsuccessful	Unsuccessful

In option d, the above set of decisions take place. In the remaining options, the decisions and the outcomes are not matched properly. Hence option d.

c. It is given that -

O: Oil industry investment is successful

Therefore the possible events which might lead to this are -

Sl No.	Oil	Municipal Bond
1	Successful	Successful
2	Successful	Unsuccessful

Since the oil industry investment is successful always, hence from the above table, number of sample points is 2.

M: Municipal Bond investment successful

Therefore the possible events which might lead to this are -

Sl No.	Oil	Municipal Bond
1	Successful	Successful
2	Unsuccessful	Successful

Since the municipal bond investment is successful always, hence from the above table, number of sample points is 2.

d. Given the elements of O: { SS, SU }

Given the elements in M: { SS, US }

Therefore from the definition of the union of sets, in the event of O union M, we would have: { SS, SU, US } i.e. 3 elements.

e. Given the elements of O: { SS, SU }

Given the elements in M: { SS, US }

Therefore from the definition of the intersection of sets, in the event of O intersection M, we would have: { SS } i.e. 1 element.

f. For the sets to be mutually exclusive they shouldn't have any common element, i.e. O intersection M should be 0. But here we have one element common in both of them. Hence they are not mutually exclusive.