The Alfred Hitchcock Hour

One of the Family (3x16)

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Dexter Dailey and his wife Joyce hire a German nursemaid named Frieda to take care of their newborn infant. Dexter treats Frieda like one of the family, because long ago she was his nursemaid when he was a child. Joyce, however, doesn't feel the same way. She becomes worried when she hears about a nurse who is wanted for a child killing in San Francisco. When she calls the murdered baby's aunt she discovers that Frieda may be the baby killer and that her child may be the next victim.