## Task A-4.4. (4 points)

In one box, there are three blue and one red ball, and in another box, there are three red and one blue ball. First, we transfer one (randomly selected) ball from the first box to the second, and then we draw one ball from the second box. What is the probability that this ball is red?
## Solution.

From the first box, we could draw a blue ball with a probability of $\frac{3}{4}$, or a red ball with a probability of $\frac{1}{4}$. Therefore, after this transfer, the second box would contain either three red and two blue balls (with a probability of $\frac{3}{4}$) or four red and one blue ball (with a probability of $\frac{1}{4}$).

In the first case, the probability of drawing a red ball is $\frac{3}{5}$, and in the second case, it is $\frac{4}{5}$. 1 point

Finally, the desired probability is $\frac{3}{4} \cdot \frac{3}{5} + \frac{1}{4} \cdot \frac{4}{5} = \frac{13}{20}$ (or $65\%$).

1 point