Hardy et al. (1934) came up with Hardy's inequality in their book. Klaassen and Wellner (2021) gave the probability version of the Hardy inequality when the parameter p > 1. Based on their work, in this paper, we assign the randomness to variables as well. When p > 1, we give some extensions of Hardy's inequality. When 0 < p < 1, we provide the corresponding Hardy inequality in probability language. Also, we show that in some circumstances, our results contain the integral form of Hardy's inequality. We give a reversed Hardy inequality for random variables as well.