The decision tree shows the profit outcomes for a coffee shop in a strong and a weak economy for next year.Suppose a third outcome is considered in which a moderate economy is 33 percent likely to occur.With this added outcome, how does the probability of a weak economy change?
A)A weak economy is now 73 percent likely.
B)A weak economy is also 33 percent likely.
C)A weak economy is now 40 percent likely.
D)A weak economy is now 0 percent likely.

Question

The decision tree shows the profit outcomes for a coffee shop in a strong and a weak economy for next year.Suppose a third outcome is considered in which a moderate economy is 33 percent likely to occur.With this added outcome, how does the probability of a weak economy change? 
A)A weak economy is now 73 percent likely. 
B)A weak economy is also 33 percent likely. 
C)A weak economy is now 40 percent likely. 
D)A weak economy is now 0 percent likely.

Quizplus · Accepted Answer

If a moderate economy has a 33% chance of occurring, then the probability of either a strong or weak economy is now 33%. Therefore, the probability of a weak economy has not changed from the original 33%, but the probability of a strong economy has decreased from 67% to 33%. This means that the remaining 33% must go to the moderate economy. To calculate the new probability of a weak economy, we need to add the probabilities of a weak economy occurring in both scenarios (0.3 * 0.3 = 0.09), and then divide by the total probability of all three scenarios:

0.33 + 0.33 + 0.09 = 0.75

Therefore, the probability of a weak economy is now 40% (0.3 + 0.09/0.75).

The Decision Tree Shows the Profit Outcomes for a Coffee