The tickets in a box are numbered from 1 to 15 inclusive. If a ticket is drawn at random and replaced and then a second is drawn at random, what is the probability that the sum of their numbers is even?

For the sum of two numbers to be even, there are two cases to be considered:

1. Both tickets are even. 7 tickets are even

Probability = 7/15 x 7/15 [with replacement]

2. Both tickets are odd. 8 tickets are odd.

Probability = 8/15 x 8/15 [with replacement]

Total Probability = 7/15 x 7/15 + 8/15 x 8/15 = 113/225 ≈ 0.502.