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 an experiment.

a$.$ How many sample points exist for this experiment?

b$.$ Show a tree diagram and list the sample points.

c$.$ Let $O=$ the event that the oil industry investment is successful and

$M=$the event that the municipal bond investment is successful. List the

sample points in $O$ and in $M.$

d$.$ List the sample points in the union of the events $(OM).$

e$.$ List the sample points in the intersection of the events $(OM).$

f$.$ Are events $O$ and $M$ mutually exclusive? Explain.