The probability that x1 + x2 + x3 is odd, is

Case I: One odd, 2 even
Total number of ways = 2 × 2 × 2 + 1 × 3 × 3 + 1 × 2 × 4 = 29.
Case II: All 3 odd
Number of ways = 2 × 3 × 4 = 24
Favorable ways = 53
Required probability = 53 / (3 × 5 × 7) = 53105