>>Dr. Barker: At Kruger Industrial Smoothing, engineering projects fall into four categories.
70 percent of projects are low risk, 20 percent are medium risk, and eight percent are high
risk, and the rest are extremely high risk. Assume that the riskiness of one project doesn’t
affect the riskiness of another project. And what do we mean by risk in this situation?
Well, it could be that risk is some measure of the, the chance that a, an engineering
project goes longer than expected, or maybe it costs more than the original bid was. It
could vary from industry to industry on what is defined by project risk, okay? So let’s
say a new project comes in. What’s the probability that that new project is medium or high risk?
Okay, so let’s first define some events. Okay? Let’s define the event – let’s
not start with E. Let’s define the event L as a low risk project, okay. So a particular
project is low risk, that event would be called L. Let’s call the medium-risk project medium
or M, okay. A high-risk project is called H. That event H is that the next project is
a high-risk project, and then finally E is what’s leftover: extremely high risk.
Okay? And we have the probabilities of each one of these, because we knew what percentages
fell into each category. We know that the probability of a low-risk project – the
next project that we see come in, the probability that it’s a low-risk project is 0.7. We
know the probability of a medium-risk project is 0.2. We know the probability of a high-risk
project is 0.08. And then finally everything else is an extremely high-risk project, okay,
and whatever else that gets us to a total probability of one is 0.02, okay? So within
a particular project these are all mutually exclusive, okay? A project can’t be simultaneously
low and medium risk itself, for one single project. And these are collectively exhaustive,
okay? There are four kinds of project risk that we could have and nothing else, okay.
So this, this captures all of the possibilities: all of the events that we could see for a particular
project. Okay, and so what we want to know is what’s the probability that a project
is medium or high risk? Okay, medium or high risk. Okay? So here or means union, okay,
and if we want this probability, the probability of medium or high risk, that is the probability
– or yeah, that’s the sum of the probabilities of medium and high risk. And we have to subtract
off the intersection between medium and high risk, okay? But what’s the intersection
between medium and high risk? We can’t have a project that’s both medium and high risk
at the same time; that just doesn’t occur. There is no intersection. Again, all of these
are mutually exclusive events. So this probability is zero. So now the probability that we have
a medium or a high-risk project is just the sum of these two probabilities. The probability
of a medium-risk project, 0.2, the probability of a high-risk project, 0.08. So that is 0.28.
So the probability that the next project that comes is either medium or high risk, 0.28.