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

With the new outcome of a moderate economy being 33% likely to occur, the sum of probabilities for all three outcomes (strong, moderate, weak) must equal 1 or 100%. So, the probabilities must be adjusted accordingly:

Strong economy: 40%
Moderate economy: 33%
Weak economy: x = 27%

Therefore, the probability of a weak economy has decreased from 33% to 27%, and the new probability of a weak economy is 27 + 6 = 33%. Therefore, choice C is the correct answer.

The Decision Tree Shows the Profit Outcomes for a Coffee