Question $2$:

A town with population $10000$ has suffered an outbreak of dragon pox, with $2\%$ of the population being infected. There is a test to diagnose the disease. If you have dragon pox, the test will correctly register 'positive' $99\%$ of the time and will yield a 'false negative' $1\%$ of the time. If you do not have dragon pox, the test will register that correctly $95\%$ of the time and will yield a 'false positive' $5\%$ of the time. Given that you tested positive for the disease, what is the probability that you actually have dragon pox? Enter your answer as a decimal $($between $0$ and $1).$ Do not enter a percent and do not use the percent symbol. Round your answer to five decimal places

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