Question 1172393
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This problem is to be solved in 3 (three) steps.



<pre>
    (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 ) =  {{{P(A_and_B) / P(B)}}} = {{{0.3/0.5}}} = {{{3/5}}} = 0.6.    <U>ANSWER</U>
</pre>


Solved step by step and explained in all details.


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In this site, there are two lessons for problems on <U>conditional probability</U>.  They are

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Conditional-probability-problems.lesson>Conditional probability problems</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/More-conditional-probability-problems.lesson>Conditional probability problems REVISITED</A> 


Read them to develop your skills and knowledge.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic &nbsp;"<U>Solved problems on Probability</U>" 
and &nbsp;"<U>Additional problems on Probability</U>". 



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.