Alright to just work through another example here,

let's take a particular case of people being audited by the IRS.

So in this particular example, lets suppose we've got an accountant.

He's got three clients who filed returns of more than $5 million for their estate.

So there is a 50% chance for each of these clients, that they're going to be audited.

Right, well if we look at what are the chances that

all three of them are going to be audited?

So client one and client two and client three all audited.

All right, well, 50% chance for client one, and a 50% chance for client two.

So we're going to multiply those together.

And a 50% chance for client three turns out that that joint probability of

all three being audited is going to be 12.5%.

All right, what about none of them being audited?

Well, client one is not audited, client two is not audited, and

client three is not audited.

It's actually going to turn out to be the same because we're dealing with a 50%

probability here.

But it's the probability that client one's not audited,

multiplied by the probability client two is not audited,

multiplied by the probability of client three not being audited.

And then how likely is it that at least one of these clients is audited?

So we're not saying that just one is audited,

we're saying at least one of them.

It could be one, it could be two, it could be all three of them.

Well we can actually use the compliment rule here to say what's the compliment

of at least one of them being audited?

It's the probability that none of them are audited.

So it's 1 minus 12.5% gives us the 87.5%.

The big assumption that we're making here

is that these observations are independent of each other.

If we have a reason to believe that the likelihood that client one is audited is

linked to the likelihood that client two is audited, this is going to break down,

we're going to have to use the more general multiplication rule.