The obdurate persistence of rationalism

Marcus J. is a mathematician extraordinaire. Because it is no longer politically correct to use ivory, the tower in which he is hermetically sealed is made of recycled plastics. In his tower, walled off from the rest of the world, he pursues mathematics. Having started out modestly with theorizing that flipping two coins will yield two heads with a probability of 25%, he has lately gone on to more ambitious projects. Most recently he has published a paper, earning wide acclaim, in which he has theorized that, since there are exactly four possible pairings (female-female; male-male; female-male; and male-female) of adult human beings, there is, then, a 25% probability that a household is headed by two women; a 25% probability that a household is headed by two men; and a 50% probability that a household is headed by one man and one woman.
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