15.6.8 Definition and properties of probability

Problem: There are white and black balls in two boxes. There are 2 black and 1 white balls in the \( 1^{\text {st }} \) box, and 3 white and 3 black balls in the \( 2^{\text {nd }} \) box. Two balls are randomly chosen from each of the two boxes and put them in the \( 3^{\text {rd }} \) empty box. It turns out that there are balls of both colours in the \( 3^{\text {rd }} \) box. Find the probability that a ball, randomly chosen from the \( 3^{\text {rd }} \) box, will be white.