An instructor has a question bank consisting of 300 easy True/False questions, 200 difficult True/False questions, 500 easy

.: Let $E$ : 'it is an easy question' and $F$ : 'it is multiple choice question'

then $E \cap F$ : 'it is an easy multiple choice question'

Total number of questions $= 300 + 200 + 500 + 400 = 1400$

$\therefore$ $P(E \cap F) = \cfrac{{500}}{{1400}} = \cfrac{5}{{14}}$

and $P\left( {F = \cfrac{{500 + 400}}{{1400}} = \cfrac{9}{{14}}} \right)$

Hence, required probability $= P(E|F) = \cfrac{{P(E \cap F)}}{{p(F)}} = \cfrac{{5/14}}{{9/14}} = \cfrac{5}{9}$