Most infants show no clear hand preference (left- or right-handedness) for years. Instead, many seem to alternate between favoring the right hand and the left hand, using the left hand for several months, then the right, and then both equally for a time. By age 2, some have established a clear hand preference, although many continue alternating for several more years. In general, about 10-13% will ultimately be left-handed.
Ames, L., & Ilg, F. (1964). The developmental point of view with special reference to the principle of reciprocal neuromotor interweaving. Journal of Genetic Psychology, 105, 195