Touch two red balls: 3 red and 3 white, then the possibility of touching the first red ball is1/2; When touching the second one, it is 2 red and 3 white, so the possibility of red ball when touching the second one is 2/5; The result of multiplication is 1/5.

Touch one red and one white: Similarly, the possibility of touching the first red ball is1/2; When touching the second one, it is 2 red and 3 white, so the possibility of touching the second one is 3/5; Multiply by 3/ 10. The probability that the first one touches the white ball and the second one touches the red ball is the same, so it adds up to 3/5.

Solve with probability:

Two red balls (C3 takes 2)/(C6 takes 2) =1/5;

One red and one white (C3 is 1 * C3 is 1)/(C6 is 2)=3/5.