A self-administered pregnancy test detects 85% of those who are pregnant but does not detect pregnancy in 15%. It is 90% accurate in indicating women who are not pregnant but indicates 10% of this group as being pregnant. Suppose it is known that 1% of the women in a neighborhood are pregnant. If a woman is chosen at random from those living in this neighborhood, and if the test indicates she is pregnant, what is the probability that she really is?
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