# Thread: set question from Goldberg's book

1. ## set question from Goldberg's book

I am working my way through Goldberg's Probability: An Introduction and am stuck on problem 4.13, chapter 2. The problem states: "Let E and F be any two events. Suppose the numbers P(E), P(F), and are known. Find numbers for these terms for the following probabilities:... ."

I can only get as far as:

I have no idea how to convert the right most part, the intersection of the compliment of E and F into the knowns. I have tried DeMorgan's laws with no help.

Oh, the answer in the back of the book is:

2. ## Re: set question from Goldberg's book

Originally Posted by ptremblay

I can only get as far as:

I'm assuming your left hand side is supposed to be

I like your first step. The second step I like one part of it (writing P(E') = 1-P(E)) but I don't like the very last part (how can an event be intersected with a probability?)

One hint I'll give is that hopefully you can recall that
and that and are disjoint. So turn that into a probability statement and see if you can use that to finish up what you want to show.

3. ## Re: set question from Goldberg's book

Woops! I should double check my work. Meant to write:

The text book did not give either of your identities. So:

I never would have gotten this without your help, since, as I stated, the book did not give the identities. (I hate when textbooks give you problems they haven't readied you to solve.)

Thanks!

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