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# Probability of being under budget and within schedule

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You are deciding whether or not you want to manage a new project for your company. Since you are very ambitious, you want to decide whether this is in your best interest. You know that to be successful as a PM, your project must come in within the approved budget and be completed within the approved schedule. You do some research and learn the following:

a. The probability of a project in your company being under budget, based on historical data, is 60%.
b. The probability of a project in your company being within schedule, based on historical data, is 60%.

Part a: With only this information, what is the probability that a project manager will be successful? Ignore the fact that you are much smarter than other project managers, work harder, and doggone it, people like you.

Part b: You decide to do some more research and discover that being on schedule and within budget are not independent events. The probability of being both over budget and over schedule is 25%. What is the probability of being successful based on this new information?

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Part a:

When considering the probability that the project in your company will be under budget is 60%, the probability is 0.6.
When considering the probability that the project in your company will within schedule is 60%, the probability is 0.6.

So, the probability that both the project in your company will be under budget and will be within schedule will be = the probability that the project will be under budget multiplied by the probability that project will be within schedule. So, 0.6 X 0.6 = 0.36. The probability that the project manager will be successful will be 0.36. This can be expressed as 36%.

Part b:

When we find that the probability of being both over the budget and over schedule is 25%, or 0.25. Now the probability of being over the budget is 1 - 0.6 = 0.4, similarly, the probability of being over schedule is also 1 - 0.6 = 0.4.

So, from the theory of joint probability, the probability of failure of the project is the probability of being over the budget plus the probability of being over schedule, minus the joint probability of being both over the budget and over schedule.

We get from above, the probability of failure of the project is: 0.4 + 0.4 - 0.25 = 0.55.
So, the probability of success is 1 - 0.55 = 0.45.

The probability of success based on this information is 0.45. This can be expressed as 45%.

References:

www.investopedia.com ? Tutorialswww.investopedia.com ? Dictionaryhttp://math.youngzones.org/joint.htmlwww.mathgoodies.com/lessons/vol6/independent_events.htmwww.stats.gla.ac.uk/steps/glossary/probability.htmlwww.cc.gatech.edu/~lebanon/notes/condProb.pdf

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