Question 1163268
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<pre>

(i)  Use the general formula of the Probability theory

         P(A or B) = P(A) + P(B) - P(A and B).


     Substitute the given data to the formula

         {{{3/4}}} = {{{1/2}}} + {{{2/3}}} - P(A and B).


     It gives you

          P(A and B) = {{{1/2 + 2/3 - 3/4}}} = {{{6/12 + 8/12 - 9/12}}} = {{{(6+8-9)/12}}} = {{{5/12}}}.     <U>ANSWER</U>



(ii)  The given equality  P(A|B) = {{{2/5}}}  means, by the definition of the conditional probability, that

          P(A and B)/P(B) = {{{2/5}}}.


      It implies that

           P(A and B) = {{{(2/5)*P(B)}}} = {{{(2/5)*(2/3)}}} = {{{4/15}}}.     <U>ANSWER</U>


      Notice that the given value  P(A) = {{{1/2}}}  is IRRELEVANT to the solution of the part (ii).
</pre>

Solved.


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