Need Solution with steps for this Probability Question?

To select a box :
P(box I) = P(box II) = P(box III) = 1/3

To draw a ball from a box :
P(red ball | box I) = 7/(7 + 5 + 4) = 7/16
P(red ball | box II) = 5/(5 + 6 + 3) = 5/14
P(red ball | box III) = 4/(4 + 3 + 2) = 4/9


P([One of boxes is selected] and [a red ball is drawn from this box])
= P([box I] and [red ball]) + P([box II] and [red ball]) + P([boxIII] + [red ball])
= (1/3) × (7/16) + (1/3) × (5/14) + (1/3) × (4/9)
= 1249/3024