While willywutang was trying to be clever by using only two condoms to satisfy three women, increased friction between overlapped latex layers produces a tear and a dangerous accident! He then becomes very worried about having contracted an STD, especially since one of the women was 'looked like she could have an STD. Although a random person has only probability 0.001 of having an STD, poor willywutang just can't sleep over those odds. Frantically he hustles to the nearest drugstore, to purchase the ACME All-Purpose STD Checker. The packaging boasts a 0.93 correctness probability. That is, if the user has an STD, the ACME STD Checker will return positive 93% of the time; if the user does not have an STD, it will return negative 93% of the time. Willywutang returns home and uses the checker in his bathroom.

To his dismay, the results are positive.

Assuming that willywutang's promiscuity on average is identical to that of a randomly chosen person, what is the probability that willywutang has STDs?

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