Almost all orbit types imply period-3

A special case of Sarkovskii's theorem says that if a continuous function has a period-3 point then it has periodic points of every order. In this note we will investigate how often orbit types of period-n guarantee a period-3 point. An informal statement of our result is that as n goes to infinity the probability that a period-n orbit guarantees a period-3 point converges to 1.