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I.e., on realizing that the strangers were God's messengers, and that she and Abraham had nothing to fear from them (Zamakhshari): hence the interpolation of the words "with happiness". This differs from the Biblical statement (Genesis xviii, 12-15), according to which Sarah "laughed within herself" at the announcement that she, an old woman, would give birth to a son: for in the above Qur'anic passage this announcement comes after the statement that she laughed, and is introduced by the conjunctive fa, which in this context denotes "and thereupon" or "whereupon".
She laughed after her husband was assured that the guests intended no harm or when she heard the news of the imminent destruction of the sinful people of Lot.
The narrative is very concise, and most of the details are taken for granted. We may suppose that the angels gave the news first to Abraham, who was already, according to Gen. xxi 5, a hundred years of age, and his wife Sarah was not far short of ninety (Gen. xvii. 7). She was probably screened. She could hardly believe the news. In her scepticism (some say in her joy) she laughed. But the news was formally communicated to her that she was to be the mother of Isaac, and through Isaac, the grandmother of Jacob. Jacob was to be a fruitful tree, with his twelve sons. But hitherto Abraham had had no son by her, and Sarah was past the age of child-bearing. "How could it be?" she thought.