Question 1174934
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(a) From one side,  P(or) = 1 - {{{5/65}}} = {{{60/65}}}.


    From the other side,


        P(or) = P(junior) + P(history) - P(both),

    or

       {{{60/65}}} = {{{37/65}}} + {{{38/65}}} - P(both).


    THEREFORE,

       P(both) = {{{37/65 + 38/65 - 60/65}}} = {{{15/65}}} = {{{3/13}}}.    <U>ANSWER</U>



(b)   P(junior|history) = {{{P(both)/P(history)}}} = {{{((3/13))/((38/65))}}} = {{{((15/65))/((38/65))}}} = {{{15/38}}}.    <U>ANSWER</U>
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Solved.  &nbsp;&nbsp;//  &nbsp;&nbsp;All questions are answered.