document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170935>Question 1170935</A>: <I><SPAN STYLE=\"word-break: break-all;\"> #3 3. It is estimated that 4% of people who spend time in the woods will get Lyme disease. For people with Lyme disease, the test to determine if you have it is will give a positive reading 97% of the time. Of people who do not have Lyme disease, the same test will give a negative rating of 92% of the time. Make a tree diagram for this problem and then answer the following questions. Find the probability that A) a person gets a positive reading B) a person gets a negative reading C)  a person gets a positive reading and they have  Lyme disease D) a person gets a negative reading and they have  Lyme disease E ) a person gets a negative reading and they don’t have Lyme diseasePositive </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #851042 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=851042\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Absolutely! Let's break down this problem step by step.\r<BR>\n" );
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document.write( "**1. Tree Diagram**\r<BR>\n" );
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document.write( "* **First Branch:**<BR>\n" );
document.write( "    * Lyme Disease (L): Probability = 0.04 (4%)<BR>\n" );
document.write( "    * No Lyme Disease (¬L): Probability = 0.96 (96%)<BR>\n" );
document.write( "* **Second Branch (for Lyme Disease):**<BR>\n" );
document.write( "    * Positive Test (+): Probability = 0.97 (97%)<BR>\n" );
document.write( "    * Negative Test (-): Probability = 0.03 (3%)<BR>\n" );
document.write( "* **Second Branch (for No Lyme Disease):**<BR>\n" );
document.write( "    * Positive Test (+): Probability = 0.08 (8%) (Since negative is 92%)<BR>\n" );
document.write( "    * Negative Test (-): Probability = 0.92 (92%)\r<BR>\n" );
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document.write( "**2. Calculations**\r<BR>\n" );
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document.write( "Let's calculate the probabilities of each outcome:\r<BR>\n" );
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document.write( "* P(L+) = P(L) * P(+|L) = 0.04 * 0.97 = 0.0388<BR>\n" );
document.write( "* P(L-) = P(L) * P(-|L) = 0.04 * 0.03 = 0.0012<BR>\n" );
document.write( "* P(¬L+) = P(¬L) * P(+|¬L) = 0.96 * 0.08 = 0.0768<BR>\n" );
document.write( "* P(¬L-) = P(¬L) * P(-|¬L) = 0.96 * 0.92 = 0.8832\r<BR>\n" );
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document.write( "**3. Answering the Questions**\r<BR>\n" );
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document.write( "A)  **Probability of a positive reading:**\r<BR>\n" );
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document.write( "* P(+) = P(L+) + P(¬L+) = 0.0388 + 0.0768 = 0.1156\r<BR>\n" );
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document.write( "B)  **Probability of a negative reading:**\r<BR>\n" );
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document.write( "* P(-) = P(L-) + P(¬L-) = 0.0012 + 0.8832 = 0.8844\r<BR>\n" );
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document.write( "C)  **Probability of a positive reading and having Lyme disease:**\r<BR>\n" );
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document.write( "* This is P(L+), which we already calculated: 0.0388\r<BR>\n" );
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document.write( "D)  **Probability of a negative reading and having Lyme disease:**\r<BR>\n" );
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document.write( "* This is P(L-), which we already calculated: 0.0012\r<BR>\n" );
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document.write( "E)  **Probability of a negative reading and not having Lyme disease:**\r<BR>\n" );
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document.write( "* This is P(¬L-), which we already calculated: 0.8832\r<BR>\n" );
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document.write( "**Summary of Answers**\r<BR>\n" );
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document.write( "A)  0.1156<BR>\n" );
document.write( "B)  0.8844<BR>\n" );
document.write( "C)  0.0388<BR>\n" );
document.write( "D)  0.0012<BR>\n" );
document.write( "E)  0.8832<BR>\n" );
document.write( " </SPAN>\n" );
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