This problem is familiarly known as the "probability of independent events."
the event that the first ball is blue, and
the event that the second ball is blue.
In the beginning, there are 35 balls in the box, 12 of which are blue. Therefore, expressing it into a probability form as
After the first selection, the ball was returned to the box making the number of balls in the box still equal to 12 blue, 14 red, and 9 yellow balls. So
Thus, multiplying the two probabilities yields
the event that the first ball is red, and
the event that the second ball is yellow.
Again there are 35 balls, 14 of which are red:
For the second selection to be a yellow ball (as which the returning of the first ball to the box is allowed),