14/27

case 1, the two numbers Alan got are different, the chance for Beti is 1-4/6 * 4/6=5/9

case 2, the two numbers Alan got are identical, the chance for Beti is 1/6+1/6=1/3

The probability to get different two numbers for Alan is 5/6

The probability to get two identical numbers is 1/6

5/6 * 5/9 +1/6 * 1/3=25/54+1/18=28/54=14/27