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 Oil Industry Municipal Bond Successful Successful Successful Unsuccessful Unsuccessful Successful Unsuccessful Unsuccessful a. How many sample points exist for this experiment? b. Choose a tree diagram. Let A. B. C. D. c. Let and . How many sample points exist for O? How many sample points exist for M? d. Identify the sample points in the union of the events ( ). e. Identify the sample points in the intersection of the events ( ). f. Are events O and M mutually exclusive?

Answer 1

a. How many sample points exist for this experiment?

There are 4 sample points exists for this experiment.

b. Choose a tree diagram.

c. How many sample points exist for O?

consider individually
let Os and Of be the events where oil industry investment is successful and failure respectively if O is taken alone
similarly Ms and MF be the events where municipal investment is successful and failure respectively if M is taken alone

the sample space of the event taken both at a time is {(Os,Ms),(Of,Ms),(Os,Mf),(Of,Mf)}

The third and fourth points represent the sample points where oil industry investment was successful
therefore O ={(Os,Ms),(Os,Mf)}

How many sample points exist for M?

The first two points represent the sample points where municipal investment was successful
therefor M = {(Os,Ms),(Of,Ms)}

d. Identify the sample points in the union of the events ( ).

Since O = the event that the oil industry investment is successful and M = the event that the municipal bond is successful, O and M are:

$\\O=\left \{ OM,OM^c \right \} \\M=\left ( OM,O^cM \right ) \\(O\cup M)=\left \{ OM,OM^c,O^cM \right \}$

e. Identify the sample points in the intersection of the events ( ).

$\\O=\left \{ OM,OM^c \right \} \\M=\left ( OM,O^cM \right ) \\(O\cap M)=\left \{ OM \right \}$

f. Are events O and M mutually exclusive?

No

as O intersection M is not empty set