document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1186369>Question 1186369</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bush pilot faces the following situation. His single-engine aircraft is on fire. He could attempt to <BR>\n" );
document.write( "crash land on the beach ahead, in which case he will need assistance or he could attempt to reach <BR>\n" );
document.write( "an emergency strip at which he can land safely and assistance will be available. Using the estimates <BR>\n" );
document.write( "given below what should he do if his objective is to stay alive?<BR>\n" );
document.write( "(a) odds on reaching emergency strip versus mid-air explosion 1:4;<BR>\n" );
document.write( "(b) probability of surviving mid-air explosion 0;<BR>\n" );
document.write( "(c) probability of reaching beach 0.8;<BR>\n" );
document.write( "(d) probability of surviving beach landing 0.5;<BR>\n" );
document.write( "(e) probability of receiving necessary assistance after a beach landing<BR>\n" );
document.write( " by air rescue 0.3,<BR>\n" );
document.write( " by passing boat 0.2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849451 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=849451\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to break down the pilot's decision-making process:\r<BR>\n" );
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document.write( "**1. Probability of Reaching the Emergency Strip:**\r<BR>\n" );
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document.write( "*   The odds of reaching the strip vs. mid-air explosion are 1:4. This means the probability of reaching the strip is 1/(1+4) = 1/5 = 0.2.\r<BR>\n" );
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document.write( "**2. Probability of Surviving the Emergency Strip Landing:**\r<BR>\n" );
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document.write( "*   If he reaches the strip, he lands safely, and assistance is available. So, the probability of survival is 1.\r<BR>\n" );
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document.write( "**3. Probability of Surviving the Beach Landing:**\r<BR>\n" );
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document.write( "*   Probability of reaching the beach: 0.8<BR>\n" );
document.write( "*   Probability of surviving the beach landing *given* he reaches the beach: 0.5<BR>\n" );
document.write( "*   Probability of surviving the beach landing *and* reaching the beach: 0.8 * 0.5 = 0.4\r<BR>\n" );
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document.write( "**4. Probability of Receiving Assistance After a Beach Landing:**\r<BR>\n" );
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document.write( "*   Probability of assistance by air rescue: 0.3<BR>\n" );
document.write( "*   Probability of assistance by passing boat: 0.2<BR>\n" );
document.write( "*   Probability of *at least* one of these assisting: 0.3 + 0.2 - (0.3 * 0.2) = 0.5 - 0.06 = 0.44\r<BR>\n" );
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document.write( "**5. Overall Probability of Survival (Beach Landing):**\r<BR>\n" );
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document.write( "*   Probability of surviving beach landing *and* getting assistance: 0.4 * 0.44 = 0.176\r<BR>\n" );
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document.write( "**6. Overall Probability of Survival (Emergency Strip):**\r<BR>\n" );
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document.write( "*   Probability of reaching the strip: 0.2<BR>\n" );
document.write( "*   Probability of surviving the landing: 1<BR>\n" );
document.write( "*   Overall survival probability: 0.2 * 1 = 0.2\r<BR>\n" );
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document.write( "**7. Decision:**\r<BR>\n" );
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document.write( "The pilot has a higher chance of survival (0.2 or 20%) if he attempts to reach the emergency strip compared to attempting a beach landing (0.176 or 17.6%).\r<BR>\n" );
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document.write( "**Therefore, the pilot should attempt to reach the emergency strip.**<BR>\n" );
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