# Decision Tree: PMP Questions to Study

What’s your favorite type of tree? Is it a Christmas tree? A deciduous tree? An apple tree? Well, my favorite tree is the decision tree, and I’m here to convince you that it should be yours too.

Decision trees are a key part of expected monetary value (EMV) analysis, which is a tool & technique in the Perform Quantitative Risk Assessment process of Risk Management. The goal for this article is to first give you a brief introduction to decision trees, then give you a few sample questions. Then you’ll pretty much know every you need to know about EMV and decision trees for the PMP exam.

## How Decision Trees Work

Decision trees help with quantitative analysis. Before we take a look at a decision tree, you need to understand the decision tree key, which is pictured below.

Next, imagine a make-or-buy situation. If you buy the product, then you know it will cost you \$5 million. However, you could also make the product. If there’s strong market demand, you could actually make \$10 million for your company. If there’s weak market demand, you might lose \$20 million (but you still have the product at least!). There’s a 75% chance there will be strong market demand and 25% chance there will be weak market demand. What should you do?

Well first, build a decision tree! Here’s the incomplete decision tree based on the scenario above:

If you buy the product, you’ll spend \$5 million. So your EMV is -\$5M. Easy!

Now, you need a formula to figure out your EMV of making the product. Figure out the weighted average:

75% * \$10M + 25% * -\$20M
= \$7.5M + -\$5M
= \$2.5M

Assuming your company is risk-neutral (remember, that’s a key assumption!), then you’ll choose to make the product, because your EMV for making (\$2.5M) is greater than your EMV for buying (-\$5M). We continue to emphasize the risk-neutral part because even though the EMV of making is \$2.5M, you could actually lose \$20M. Eek!

Here’s how you apply that logic to your decision tree:

The PMBOK guide does a clear job of describing decision trees on page 339, if you need additional background.

## PMP Decision Tree Questions

For this problem, build your own decision tree to confirm your understanding. On the PMP exam, you may be asked to analyze an existing decision tree. To really make sure you understand the concept, however, it’s important to draw and analyze from scratch.

Your company wants to decide between Investment A, which will cost \$100K upfront, and Investment B, which will cost \$150K upfront. If the economy performs well, Investment A will bring in \$750K for your company, but if the economy performs poorly, then it will lose \$250K for your company. If the economy performs well, Investment B will bring in \$850K for your company, but if the economy performs poorly, then it will lose \$300K for your company. There’s a 60% chance of a strong market and a 40% chance of a weak market.

1. Assuming your company is risk-neutral, which option should you choose?

A. Investment A
B. Investment B
C. Choose neither investment.
D. Get a second opinion.

2. What is the EMV of Investment A?

A. \$750K
B. -\$250K
C. \$250K
D. -\$100K

3. If the EMV of Investment B increases to \$260K, which option should you choose?

A. Investment A
B. Investment B
C. Choose neither investment.
D. Seek Expert Judgment.

4. If the chance of a strong or weak market changes to 50/50, what is the new best option?

A. Investment A
B. Investment B
C. Choose neither investment.
D. Seek Expert Judgment.

Well, draw your decision tree! That’s going to be the most important part of answering this question.

A key mistake that some people make when developing decision trees is putting the chance node before the choice node. Remember, the decision tree should logically flow — you have to make your investment decision before knowing whether the market will be strong or weak.

1. A. Investment A. Because the EMV of Investment A is greater than the EMV of Investment B, you should choose Investment A.

2. C. \$250K. Your decision tree helped you determine this one as well. Sometimes on the PMP exam, the question will ask for the EMV of a particular choice rather than which choice is best.

3. B. Investment B. A problem on the PMP exam might also give you a completed decision tree, then ask you what you should do if a particular factor changes. In this case, recalculate whatever part of the decision tree you need to and answer it.

4. A. Investment A. Same logic as in number three. The good news is that decision tree problems can’t get much more complicated than that.

My advice would be to master the decision tree concepts and then move on. You may have one, two, or possible no decision tree questions on your PMBOK exam. The good news is that after reading this article, you’ve now experienced easy, moderate, and difficult decision tree questions. Unlike many PMBOK concepts, this one doesn’t get much tougher! Now that’s a reason to celebrate.

Do you feel like a decision tree expert? Dare I say that you are a decision tree arborist? Anyway, comment below with your thoughts, and we’ll discuss!