$10 \%$ of the population in a town is $\mathrm{HIV}^{+}$. A new diagnostic kit for HIV detection is available; this kit correctly identifies HIV $^{+}$ individuals $95 \%$ of the time, and HIV ' individuals $89 \%$ of the time. A particular patient is tested using this kit and is found to be positive. The probability that the individual is actually positive is

$10 \%$ of the population in a town is $\mathrm{HIV}^{+}$. A new diagnostic kit for HIV detection is available; this kit correctly identifies HIV $^{+}$ individuals $95 \%$ of the time, and HIV ' individuals $89 \%$ of the time. A particular patient is tested using this kit and is found to be positive. The probability that the individual is actually positive is

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