The world had been harmed by a widespread Z-virus, which already turned 10% of the world's population into zombies.

The scientists then invented a test kit with the sensitivity of 90% and specificity of 70%: 90% of the infected people will be tested positive while 70% of the non-infected will be tested negative.

If the test kit showed positive result, what would be the probability that the tested subject was truly zombie?

If the solution is in a form of \(\dfrac{a}{b}\), where \(a\) and \(b\) are coprime positive integers, submit your answer as \(a+b\).

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