Suppose that
Box-I contains \( 8 \) red, \( 3 \) blue and \( 5 \) green balls,
Box-II contains \( 24 \) red, \( 9 \) blue and \( 15 \) green balls,
Box-III contains \( 1 \) blue, \( 12 \) green and \( 3 \) yellow balls,
Box-IV contains \( 10 \) green, \( 16 \) orange and \( 6 \) white balls.
A ball is chosen randomly from Box-I; call this ball \( b \). If \( b \) is red then a ball is chosen randomly from Box-II, if \( b \) is blue then a ball is chosen randomly from Box III, and if \( b \) is green then a ball is chosen randomly from Box-IV. The conditional probability of the event ‘one of the chosen balls is white’ given that the event ‘at least one of the chosen balls is green’ has happened, is equal to:
