Analyze the following decision tree.After determining the missing probabilities,identify which alternative (Option 1 or Options 2)has the higher expected payoff.What is the expected payoff? .
A)Option 1,with an expected payoff of less than $35
B)Option 1,with an expected payoff of no less than $35
C)Option 2,with an expected payoff of less than $35
D)Option 2,with an expected payoff of more than $35

Question

Analyze the following decision tree.After determining the missing probabilities,identify which alternative (Option 1 or Options 2)has the higher expected payoff.What is the expected payoff? . 
A)Option 1,with an expected payoff of less than $35 
B)Option 1,with an expected payoff of no less than $35 
C)Option 2,with an expected payoff of less than $35 
D)Option 2,with an expected payoff of more than $35

Quizplus · Accepted Answer

To determine the expected payoff for each option, we need to calculate the weighted average of the payoff for each possible outcome.

For Option 1: 
- If Event A occurs with a probability of 0.4, the payoff is $50. 
- If Event B occurs with a probability of 0.6, the expected payoff is: 
      - $30 x 0.5 + $60 x 0.5 = $45 
The overall expected payoff for Option 1: 
0.4 x $50 + 0.6 x $45 = $47

For Option 2: 
- If Event A occurs with a probability of 0.4, the payoff is $40. 
- If Event B occurs with a probability of 0.6: 
    - If Event C occurs with a probability of 0.6, the expected payoff is: 
         - $20 x 0.6 + $80 x 0.4 = $52 
    - If Event D occurs with a probability of 0.4, the expected payoff is: 
         - $50 x 0.4 + $70 x 0.6 = $62 
The overall expected payoff for Option 2: 
0.4 x $40 + 0.6 x ($52 x 0.6 + $62 x 0.4) = $51.12

Therefore, Option 2 has the higher expected payoff of $51.12 and is the best choice.

Analyze the Following Decision Tree