Analyze the following decision tree.Determine the missing probabilities,and identify the alternative that maximizes the expected payoff.
A)Option 1,with an expected payoff of less than $25
B)Option 1,with an expected payoff of $25 or more
C)Option 2,with an expected payoff of less than $25
D)Option 2,with an expected payoff of $25 or more

Question

Analyze the following decision tree.Determine the missing probabilities,and identify the alternative that maximizes the expected payoff. 
A)Option 1,with an expected payoff of less than $25 
B)Option 1,with an expected payoff of $25 or more 
C)Option 2,with an expected payoff of less than $25 
D)Option 2,with an expected payoff of $25 or more

Quizplus · Accepted Answer

- The missing probability for "Event 1" is calculated as follows: 
    - P(Event 1) = 1 - P(Not Event 1) = 1 - 0.2 = 0.8
- The missing probability for "Event 2" is calculated as follows: 
    - P(Event 2) = 1 - P(Not Event 2) = 1 - 0.6 = 0.4
- The expected payoffs for each option are calculated as follows: 
    - Option 1: 
        - Expected payoff = P(Event 1) × ($10,000) + P(Not Event 1) × [P(Event 2) × ($5,000) + P(Not Event 2) × ($0)] 
        - Expected payoff = 0.8 × ($10,000) + 0.2 × [0.4 × ($5,000) + 0.6 × ($0)] = $8,000
    - Option 2: 
        - Expected payoff = P(Event 1) × ($0) + P(Not Event 1) × [P(Event 2) × ($25,000) + P(Not Event 2) × ($0)] 
        - Expected payoff = 0.8 × ($0) + 0.2 × [0.4 × ($25,000) + 0.6 × ($0)] = $2,000
- Therefore, the best choice is Option 2, with an expected payoff of $2,000 or more.

Analyze the Following Decision Tree