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In a certain community, 8 perce
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<!DOCTYPE html PUBLIC "-//ABISOURCE//DTD XHTML plus AWML 2.2//EN" "http://www.abisource.com/2004/xhtml-awml/xhtml-awml.mod"><html xmlns="http://www.w3.org/1999/xhtml" xmlns:awml="http://www.abisource.com/2004/xhtml-awml/"> <head> </head> <body> <div> <p> <span style="font-weight:bold;font-size:16pt;font-family:'Times New Roman';color:#333333;background:#ffffff">Probability</span> </p> <p> <span style="font-weight:bold;font-size:16pt;font-family:'Times New Roman';color:#333333;background:#ffffff">Q</span><span style="font-weight:bold;font-size:18pt;font-family:'Times New XXXXX';color:#XXXXXX;background:#XXXXXX"></span><span style="XXXX-size:14pt;font-family:'XXXXX New Roman';color:#333333;XXXXXXXXXX:#XXXXXX"></span><span style="XXXX-size:XXXX;font-family:'XXXXX XXX Roman';XXXXX:#333333;background:#XXXXXX">XX a certain community, 8 XXXXXXX of XXX XXXXXX XXXX XX have diabetes. If a XXXXXX service</span><span style="XXXX-size:12pt;XXXX-family:'XXXXX New Roman';color:#XXXXXX"></span><span style="font-XXXX:12pt;XXXX-XXXXXX:'Times XXX XXXXX';XXXXX:#333333;background:#ffffff">in XXXX XXXXXXXXX correctly diagnoses 95 percent XX XXX XXXXXXX XXXX XXXXXXXX XX having the disease XXX incorrectly XXXXXXXXX X percent of all XXXXXXX XXXXXXX diabetes XX XXXXXX the disease, find the probabilities that, (a) the community health service will XXXXXXXX an adult XXXX 50 XX having XXXXXXXX. (b) a person XXXX XX XXXXXXXXX by XXX XXXXXX XXXXXXX XX XXXXXX XXXXXXXX XXXXXXXX has XXX XXXXXXX.</span> </p> <p> <span style="font-XXXXXX:XXXX;XXXX-XXXX:16pt">XXX.</span> </p> <p> <span style="font-XXXX:12pt">XXX XXXXX of a XXXXXX XXXX XX diagnosed XX XXX health service XX</span><span style="font-XXXXXX:XXXX;XXXX-XXXX:12pt">A</span> </p> <p> <span style="XXXX-size:12pt">XXX event that an adult XXXX XX XXXXXXXX XXX the XXXXXXXX XX</span><span style="font-XXXXXX:XXXX;XXXX-XXXX:12pt">B1</span> </p> <p> <span style="XXXX-XXXX:12pt">The event that an XXXXX over XX XXXX XXX have XXX XXXXXXXX be</span><span style="XXXX-weight:XXXX;font-size:XXXX">B2</span> </p> <p> <span style="XXXX-size:XXXX">So X(XX) = 0.08</span> </p> <p> <span style="font-size:12pt">XXX X(XX) = 1 − X(XX) = X − 0.08 = X.92</span> </p> <p> <span style="XXXX-size:12pt">The health service in XXXX community XXXXXXXXX XXXXXXXXX XX XXXXXXX of all persons XXXX XXXXXXXX as having the disease XXX XXXXXXXXXXX XXXXXXXXX 2 percent of all XXXXXXX XXXXXXX diabetes as having XXX XXXXXXX</span> </p> <p> <span style="XXXX-size:12pt">So, X(A|B1) = X.95 and P(X|B2) = X.XX.</span> </p> <p> <span style="font-XXXXXX:XXXX;font-size:XXXX">(a)</span><span style="font-size:12pt"> The probabilities XXXX, XXX XXXXXXXXX health XXXXXXX XXXX XXXXXXXX an adult over 50 as XXXXXX diabetes :</span> </p> <p style="XXXX-XXXXXX:XX.000000pt"> <span style="XXXX-XXXX:12pt">X(XX)P(A|B1) + X(B2)X(X|B2)</span> </p> <p style="text-XXXXXX:XX.XXXXXXXX"> <span style="font-XXXX:12pt">= (X.XX)(X.95) + (0.92)(0.02)</span> </p> <p style="XXXX-XXXXXX:XX.000000pt"> <span style="font-size:12pt"> =</span><span style="font-XXXXXX:bold;XXXX-size:XXXX">X.0944</span><span style="font-XXXX:12pt">.</span> </p> <p> <span style="XXXX-weight:bold;font-XXXX:12pt">(b)</span><span style="XXXX-XXXX:12pt"> The probabilities XXXX,</span><span style="font-size:XXXX;font-family:'Times XXX XXXXX';XXXXX:#XXXXXX;XXXXXXXXXX:#ffffff"> a person over XX XXXXXXXXX XX XXX health service XX having diabetes actually XXX XXX disease:</span> </p> <p style="text-XXXXXX:36.000000pt"> <span style="font-size:12pt"> X(B1|X)</span> </p> <p style="text-XXXXXX:36.000000pt"> <span style="XXXX-size:XXXX"> = X(B1)X(A|XX) X(XX)P(X|XX) + P(XX)X(A|B2)</span> </p> <p style="XXXX-XXXXXX:36.000000pt"> <span style="XXXX-XXXX:12pt"> = (0.XX)(0.95) (0.08)(0.95) + (X.XX)(X.XX)</span> </p> <p style="text-XXXXXX:36.000000pt"> <span style="XXXX-size:12pt">=</span><span style="XXXX-XXXXXX:bold;font-size:12pt">X.8051</span> </p> </div> </body> </html>">
