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February 17th, 2014, 08:50 PM  #1 
Senior Member Joined: Jan 2014 Posts: 196 Thanks: 3  A sets complement
Given, , , and Find " /> Just visualizing this, I am sure the answer is Is the correct set notation, and what is given, would this be = P(A)  P(A \cap B)" /> ? thanks! 
February 18th, 2014, 02:23 AM  #2 
Math Team Joined: Apr 2010 Posts: 2,780 Thanks: 361  Re: A sets complement
The set you want is which has area = P(A)  P(A \cap B)" />, yes.

February 18th, 2014, 04:21 AM  #3  
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: A sets complement Quote:
Imagine 10 objects in the "universe". There are 4 in A, 5 in B, and 3 in both. So there are 4 3= 1 that are in A but not in B. That would be = 1" />. There are 5 3= 2 that are in B but not in A so 10 2= 8 that are in A or not in B. That is = 8" />  
February 18th, 2014, 11:15 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 21,035 Thanks: 2271 
A = A ? (B ? B') = (A ? B) ? (A ? B'), which is a union of disjoint sets. Hence P(A) = P(A ? B) + P(A ? B'), and so P(A ? B') = P(A)  P(A ? B) = .4  .3 = .1. Similarly, P(A' ? B) = P(B)  P(A ? B) = .5  .3 = .2. As A ? B' = (A' ? B)', P(A ? B') = 1  P(A' ? B) = 1  .2 = .8. Neither calculation needs all the information given in the question. 

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