document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1195336>Question 1195336</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose a company charges a premium of $150 per year for an insurance policy for storm damage to roofs. Actuarial studies show that in case of a storm, the insurance company will pay out an average of $8000 for damage to a composition shingle roof and an average of $12,000 for damage to a shake roof. They also determine that out of every 10,000 policies, there are 7 claims per year made on composition shingle roofs and 11 claims per year made on shake roofs. What is the company’s expected value (i.e., expected profit) per year of a storm insurance policy? What annual profit can the company expect if it issues 1000 such policies?<BR>\n" );
document.write( "Determine the probability of a composition shingle roof claim out of 10,000 = ?<BR>\n" );
document.write( "Determine the probability of a shake roof claim out of 10,000 = ?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848437 by </B><A HREF=/tutors/aboutme.mpl?userid=ElectricPavlov><B>ElectricPavlov(122)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ElectricPavlov><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848437\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Calculate Probabilities:**\r<BR>\n" );
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document.write( "* **Probability of a composition shingle roof claim:** 7 claims / 10,000 policies = 0.0007<BR>\n" );
document.write( "* **Probability of a shake roof claim:** 11 claims / 10,000 policies = 0.0011\r<BR>\n" );
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document.write( "**2. Calculate Expected Payout per Policy**\r<BR>\n" );
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document.write( "* **Expected payout for composition shingle roof claims:** <BR>\n" );
document.write( "    * Probability * Payout amount = 0.0007 * $8000 = $5.60<BR>\n" );
document.write( "* **Expected payout for shake roof claims:** <BR>\n" );
document.write( "    * Probability * Payout amount = 0.0011 * $12,000 = $13.20<BR>\n" );
document.write( "* **Total expected payout per policy:** $5.60 + $13.20 = $18.80\r<BR>\n" );
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document.write( "**3. Calculate Expected Profit per Policy**\r<BR>\n" );
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document.write( "* **Expected profit per policy:** Premium - Expected payout = $150 - $18.80 = $131.20\r<BR>\n" );
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document.write( "**4. Calculate Expected Annual Profit for 1000 Policies**\r<BR>\n" );
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document.write( "* **Expected annual profit:** Expected profit per policy * Number of policies = $131.20 * 1000 = $131,200\r<BR>\n" );
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document.write( "**Therefore:**\r<BR>\n" );
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document.write( "* The company's expected profit per year of a storm insurance policy is $131.20.<BR>\n" );
document.write( "* The expected annual profit for 1000 such policies is $131,200.<BR>\n" );
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