According to a document from the Kansas Department of Health and Environment, there were 519,544 cases of COVID-19, aged 0 to 109(!), in that state in 2021. The population was 2.935 million, not that much larger than Idaho's population.  A Kansan of unknown age or other demographic data received a positive result using a rapid test with a sensitivity of 55% and a specificity of 99.5%.  What's the probability of this person being actually infected?

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