# Interpreting What Data Means

I am currently working on a problem from my statistics class. It is as follows:

The only one I had difficulty quantifying with words was problem f). How would I do that?

Also, I had originally assumed the three events were disjoint; but, by looking at the question again, I found that they aren't, because of the last piece of information given--the intersection of all of the events. I am having a hard time understanding how they are not disjoint. How can these particular three events have something in common? It just seems odd.

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How can these particular three events have something in common?

If you assume they are disjoint, that means that if the consulting firm gets Project 1 they can't possibly also get Project 2 or Project 3. That's a strong assumption! Why should getting Project 1 keep them from also getting a contract for Project 2?

As for the one you were having trouble interpreting, we have $$(A_1' \cap A_2') \cup A_3.$$ $A_1'$ means they did not get Project 1, similarly for $A_2'$. So this statement says "They failed to get both Project 1 and Project 2, or they got Project 3." And remember that the "or" is not exclusive.

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Well, how do we account for the fact, in your explanation, that $A_3$ contains portions of $A_1$ and $A_2$? –  Mack Jan 26 '13 at 18:47
@EMACK using the laws of probability, including in particular the inclusion/exclusion principle –  Jonathan Christensen Jan 26 '13 at 18:48
Oh, yes, I see clearly, now. Thank you! –  Mack Jan 26 '13 at 18:50