Presidential Problems Primary Probabilities complete solutions correct answers key

Presidential Problems Primary Probabilities complete solutions correct answers key

The US Whig Party presidential primaries are rapidly coming to a close, and candidate Barry Brassliquid has some difficult decisions about states to visit prior to the next round of primary voting.

Brassliquid has the opportunity to visit two states in consecutive time frames in his swing through the Eastern U.S. prior to the next set of primary elections.  His campaign analytics staff (the BAG – Brassliquid Analytics Group) has narrowed down his possibilities to three states: Pennsylvania, Maryland and Delaware.  The process of planning his campaign strategy is as such:  Brassliquid will first visit a state in Time Frame 1, then Twitter and other social media data can be analyzed to determine whether it was a SUCCESSFUL or UNSUCCESFUL visit.  Brassliquid will then visit a second (different) state in Time Frame 2 (in similar fashion).

Based upon the combinations of the states visited and the successes (or lack thereof), the BAG staff has estimated (via a secret formula) the expected number of delegates that Brassliquid will earn in each of the three states.  Given these estimates, your task is to determine Brassliquid’s plan for visiting/campaigning in states over the next two Time Frames.

For Time Frame 1:   the following are estimated number of delegates won in each state if visited in Time Frame 1, differentiated by successful vs. unsuccessful visit.

Pennsylvania:     Successful:         135 delegates                  Unsuccessful:    96 delegates

Maryland:         Successful:           85 delegates                Unsuccessful:    70 delegates

Delaware:         Successful:           65 delegates                Unsuccessful:    45 delegates

 For Time Frame 2:   the following are estimated number of delegates won in each state if visited in Time Frame 2, differentiated by successful vs. unsuccessful visit.

Pennsylvania:     Successful:         125 delegates                  Unsuccessful:    80 delegates

Maryland:         Successful:           80 delegates                Unsuccessful:    50 delegates

Delaware:         Successful:           50 delegates                Unsuccessful:    30 delegates

If Brassliquid doesn’t campaign in a state, then use the following for estimated delegates won.

Pennsylvania:  79 delegates.

Maryland:                       42 delegates

Delaware:                        25 delegates

So, if Brassliquid campaigns/visits Maryland in Time Frame 1 and Pennsylvania in Time Frame 2, and both visits are deemed successful, the expected number of delegates won would be:

85 + 125 + 25 = 235 delegates (see highlighted entries above)

The BAG has also estimated the likelihood of campaign.  (This is so a complete strategy can be formulated prior to the actual visits). The following table shows the probability of having the visit be SUCCESSFUL.  Note that the probability of an UNSUCCESFUL campaign is 100% minus the probability of SUCCESSFUL. Also note that Time Frame 2’s probabilities are conditional on the success of Time Frame 1’s visit.

State

Time Frame 1

Time Frame 2 – after success

Time Frame 2 – after unsuccessful visit

Pennsylvania

50%

60%

40%

Maryland

65%

50%

40%

Delaware

90%

80%

80%

Your task: Analyze strategies for Barry Brassliquid campaign choices over the next two Time Frames.  Use expected value (expected number of delegates won) as your criteria. Clearly analyze ALL possible combinations (i.e., convince the reader that you have properly applied the concept of decision tree analysis to the problem).   

When you have calculated the optimal decisions, clearly state those decisions and their ‘conditions’. (It would be expected that some form of IF-THEN-ELSE type statement comes out of your analysis, as it does in all decision trees). Leave nothing to the imagination of the assessor of this exercise.