Hey

you know what I found difficult to get my head around when I studied for the GMAT? AND, OR and NOT!

Of course, you may claim that this would cause me trouble in ordering food in restaurants or generally deciding on anything, but really it boiled down to remembering in an efficient fashion what the relationships between the probabilities of two independent events were.

For Dependent events, like either Jerry or Tom can be chosen as President, its easy : OR means ADD.

But for Independent events, you can have either happening, and you have to distinguish between A happening and B not happening, or A happening and B happening.

This gets nasty in Data Sufficiency when you are supposed to know if knowing the probability of one event, can you come up with the probability of it's combination with another event?

Enter the following diagram stage left :


Note how cleverly I have used Venn diagrams that we all know and love to explain something we all know... and fear...

Here's how it works :

We recall that P(A AND B ) is P(A) x P(B ), and that's all we need!

What's the probability of A happening, and B NOT happening? Well it's the exclusively A part of the Venn diagram! [sounds like a fashion brand, you know exclusively... ah shaddap...]

So, it's P(A) - P(A AND B ) = P (A) - P(A) x P(B ) = P(A)(1 - P(B )) = P(A) x P(NOT B )

Equally, the Probability of A OR B happening, is the union of the two sets. Because as long as either A OR B happens, we have a result.

Note that NEITHER A NOR B means NOT A AND NOT B (think about it - we need both conditions to happen at once).

So, P (A OR B )
= 1 - P (NEITHER A NOR B )
= 1 - P(NOT A AND NOT B )
= 1 - (1 - P(A)) x (1 - P(B ))

See if you can come up with another way of doing it using the fact that the union of the two sets is P(A) + P(B ) - P(A AND B )

You can quickly draw this diagram to remember how it is you figure out the relationships between probabilities of independent events.

So, how cool is this? Clearly, I'm expecting some kudos...