Question 1174251
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Events A and B are dependent. P(A)= 5/12
 and P(B given A) = 6/11. Find P(A and B).
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<pre>
P(B given A) is the conditional probability.


The standard classical designation for it is  P(B|A).


So, P(B given A) is the same as  P(B|A).


By the definition,  P(B|A) = P(B &#8745; A) / P(A).


So, you are  <U>GIVEN</U>  that   


    P(B &#8745; A) / P(A) = {{{6/11}}},   or,  which is the same,

    P(B &#8745; A) : {{{(5/12)}}} = {{{6/11}}}.


THEREFORE,

    P(B &#8745; A) = {{{(5/12)*(6/11)}}} = {{{30/132}}} = {{{5/22}}}.    <U>ANSWER</U>
</pre>

Solved.


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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.