A game involves picking coloured balls from two boxes, referred to as Box $1$ and Box $2.$

Box $1$ contains two red balls and seven green balls. Box $2$ contains four green balls and

three red balls. The balls are identical in every respect except for their colour. A blindfolded

player first chooses a box and then picks a ball. If a certain player picks a red ball, what is

the probability that the player chose from Box $1?$