Black holes have been implicated in two paradoxes that involve apparently non-unitary dynamics. According to Hawking’s theory, information that is absorbed by a black hole is destroyed, and the originally pure quantum state prior to the formation of the black hole is converted to a mixed state upon complete evaporation. Here I address one of the two, namely the apparent loss of (classical) information when it crosses the event horizon. I show that this paradox is due to a mistake in Hawking’s original derivation: he ignored the contribution of the stimulated emission of radiation that according to Einstein’s theory of blackbody radiance must accompany the spontaneous emission (the Hawking radiation). Resurrecting the contribution of stimulated emission makes it possible to calculate the (positive) classical information transmission capacity of black holes, which implies that information is fully recoverable from the radiation outside the black hole horizon. I also briefly discuss the second paradox.