Analyze the following decision tree.After determining the missing probabilities,identify which alternative (Option 1 or Option 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 Option 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 calculate the expected payoff for each option, we first need to fill in the missing probabilities: - P(Overcast and Purchase) = 0.2 - P(Overcast and Don't Purchase) = 0.3 - P(Sunny and Purchase) = 0.5 x 0.6 = 0.3 - P(Sunny and Don't Purchase) = 0.5 x 0.4 = <<0.5*0.4=0.2>>0.2 Option 1: - Purchase: $50 x 0.2 + $10 x 0.3 + $0 x 0.3 + $0 x 0.2 = $14 - Don't Purchase: $0 x 0.2 + $40 x 0.3 + $10 x 0.3 + $10 x 0.2 = $16 Expected payoff for Option 1: ($14 + $16)/2 = $15 Option 2: - Purchase: $60 x 0.2 + $5 x 0.3 + $0 x 0.3 + $0 x 0.2 = $13 - Don't Purchase: $0 x 0.2 + $45 x 0.3 + $5 x 0.3 + $5 x 0.2 = $16.5 Expected payoff for Option 2: ($13 + $16.5)/2 = $14.75 Therefore, Option 1 has a higher expected payoff than Option 2.

Analyze the Following Decision Tree