If a woman takes an early pregnancy test, she will either test positive, meaning that the test says she is pregnant, or test negative, meaning that the test says she is not pregnant. Suppose that if a woman really is pregnant, there is a 98% chance that she will test positive. Also, suppose that if a woman really is not pregnant, there is a 99% chance that she will test negative. Assume that 1000 women are to be pregnancy tested and that exactly 100 of them are pregnant. If a randomly chosen woman from this group tests positive for pregnancy, then what is the probability that she really is pregnant?
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