Under some special conditions, the P3P problem can have 1, 2, 3 and 4 solutions, and if the 3 control points and the optical center lie on a circle, the problem is indeterminate. In this paper, by the Monte Carlo approach of up to 1 million samples, it is shown that the probabilities of the P3P problem with one solution, two solutions, three solutions, and four solutions are respectively 0.9993, 0.0007, 0.0000, 0.0000. The result confirms the well-known fact that in the most cases, the P3P has a unique solution.