SOLUTION: If A and B are two events such that P(A) = 0.7 and P(B) = 0.5 and P((A u B)') = 0.1. Find P(A\B). [Note Here (A u B)' means complement of A union B]

Question 1172393: If A and B are two events such that P(A) = 0.7 and P(B) = 0.5 and P((A u B)') = 0.1. Find P(A\B). [Note Here (A u B)' means complement of A union B]
Answer by ikleyn(52778) (Show Source): You can put this solution on YOUR website!
.

This problem is to be solved in 3 (three) steps.

    (1)  From  P(A U B)') = 0.1  we have  P(A U B) = 1 - 0.1 = 0.9.



    (2)  From  P(A U B) = P(A) + P(B) - P(A and B)   we have


                  0.9   = 0.7  + 0.5  - P(A and B),  which implies


                  P(A and B) = 0.7 + 0.5 - 0.9 = 0.3.



    (3)  Having P(A and B)  just found,  we obtain for the conditional probability


             P( A | B ) =   =  =  = 0.6.    ANSWER

Solved step by step and explained in all details.

-------------

In this site, there are two lessons for problems on conditional probability. They are
    - Conditional probability problems
    - Conditional probability problems REVISITED

Read them to develop your skills and knowledge.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Solved problems on Probability"
and "Additional problems on Probability".

Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.

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