The same three boxes are used again, with the same throws of a fair die choosing the box, as in the figure. A ball is drawn and it is red. What is the probability that it came from box $2$?

Fig. 1: Three boxes side by side. Box 1 is chosen by a throw of 1 or 2 and holds 2 red and 3 green balls. Box 2 is chosen by a throw of 3, 4 or 5 and holds 4 red and 1 green ball. Box 3 is chosen by a throw of 6 and holds 1 red and 1 green ball.