To solve this problem, we can use the law of conservation of momentum, which states that the total momentum of a closed system remains constant. In this case, the closed system is the ball and the other ball.

The initial momentum of the system is:

$$P_i = m_1v_1 + m_2v_2$$

$$P_i = (0.25 kg)(1.0 m/s) + (0.15 kg)(0 m/s) = 0.25 kg m/s$$

After the collision, the ball and the other ball have velocities of 0.75 m/s and v_2, respectively. The total momentum of the system after the collision is:

$$P_f = m_1v_1' + m_2v_2'$$

$$P_f = (0.25 kg)(0.75 m/s) + (0.15 kg)v_2'$$

By the conservation of momentum, we have:

$$P_i = P_f$$

$$0.25 kg m/s = (0.25 kg)(0.75 m/s) + (0.15 kg)v_2'$$

Solving for v_2', we get:

$$v_2' = \frac{0.25 kg m/s - (0.25 kg)(0.75 m/s)}{0.15 kg} = 0.5 m/s$$

Therefore, after the collision, the other ball moves to the right with a velocity of 0.5 m/s.