An appreciable fraction of introns is thought to be involved in cellular functions, but there is no obvious way to predict which specific intron is likely to be functional. For each intron we are given a feature representation that is based on its evolutionary patterns. For a small subsets of introns we are also given an indication that they are functional. For all other introns it is not known whether they are functional or not. Our task is to estimate what fraction of introns are functional and, how likely it is that each individual intron is functional. We define a probabilistic classification model that treats the given functionality labels as noisy versions of labels created by a Deep Neural Network model. The maximum-likelihood model parameters are found by utilizing the Expectation-Maximization algorithm. We show that roughly 80% of the functional introns are still not recognized as such, and that roughly a third of all introns are functional.