(1) gets the red ball for the second time, that is, "1 gets the white ball and gets the red ball for the second time", and the probability is 2/3x 1/2= 1/3.

(2) Algorithm 1: 1-P (twice getting white balls) = 1-2/3x 1/2=2/3.

Algorithm 2: p (red ball) =P (red ball for the first time 1 and white ball for the second time) +P (white ball for the first time 1 and red ball for the second time) = 2/3x 1/2 = 2.

To sum up, the probability of getting the red ball for the second time is 1/3, and the probability of getting the red ball is 2/3.

Please adopt it, thank you!