16. Datasyitis is a strange disease with no obvious symptoms that randomly develops in $1$ in $1000$ people across the world. Fisher RX has recently developed a highly accurate diagnostic test that correctly identifies $99\\%$ of all positive cases (in other words, sensitivity = $99\\%$), and correctly identifies all unaffected individuals (in other words, specificity = $100\\%$). Let $T_\\pm$ denote the test result and $0_\\pm$ the disease state for a given individual. a) [1 point] what is the probability that you have datasyitis, that is $P(D_+)$? \\vspace {1.5cm} b) [3 points] what is the probability that you will develop datasyitis and test positive, that is $P(T_+ \\cap D_+) $? \\vspace {4cm} c) [3 points] using the law of total probability, what is the chance that you will test positive for datasyitis, that is $P(T_+) $? \\vspace {4cm} d) [4 points] Suppose that you have tested positive for datasyitis. what is the probability that you have datasyitis, that is $P(D_+ | T_+)$? Your doctor tells you that this means that you have a $99\\%$ chance of developing datasyitis, as this is the proportion of datasyitis patients that the test correctly diagnoses. Is her reasoning correct