document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203779>Question 1203779</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There is roughly an 80% chance that a person of age 20 will be alive at 65 suppose that 3 age 20's are selected at random. Find the probability that the number alive at 65 will be exactly two(2)<BR>\n" );
document.write( "b) Atleast one <BR>\n" );
document.write( "c) Atmost two<BR>\n" );
document.write( "d) Less than one <BR>\n" );
document.write( "e) Write the probability distribution </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #839627 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13209)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=839627\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The logical way to answer these questions is to do part (e) first and -- to verify that your calculations are correct -- verify that the sum of the probabilities is 1; then answer the individual questions.<br><BR>\n" );
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document.write( "NOTE!\r<BR>\n" );
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document.write( "If you are just learning how to calculate binomial probabilities, it is good practice -- if the number of cases is small -- to calculate the probabilities of all possible outcomes and verify that their sum is 1\r<BR>\n" );
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document.write( "3 of 3 alive at age 65:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%283%2C3%29%28%28.8%29%5E3%29%28%28.2%29%5E0%29=%281%29%28.512%29%281%29=.512 ALIGN=MIDDLE  ALT=\"C%283%2C3%29%28%28.8%29%5E3%29%28%28.2%29%5E0%29=%281%29%28.512%29%281%29=.512\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "2 of 3 alive at age 65:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%283%2C2%29%28%28.8%29%5E2%29%28%28.2%29%5E1%29=%283%29%28.64%29%28.2%29=.384 ALIGN=MIDDLE  ALT=\"C%283%2C2%29%28%28.8%29%5E2%29%28%28.2%29%5E1%29=%283%29%28.64%29%28.2%29=.384\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "1 of 3 alive at age 65:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%283%2C1%29%28%28.8%29%5E1%29%28%28.2%29%5E2%29=%283%29%28.8%29%28.04%29=.096 ALIGN=MIDDLE  ALT=\"C%283%2C1%29%28%28.8%29%5E1%29%28%28.2%29%5E2%29=%283%29%28.8%29%28.04%29=.096\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "0 of 3 alive at age 65:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%283%2C0%29%28%28.8%29%5E0%29%28%28.2%29%5E3%29=%281%29%281%29%28.008%29=.008 ALIGN=MIDDLE  ALT=\"C%283%2C0%29%28%28.8%29%5E0%29%28%28.2%29%5E3%29=%281%29%281%29%28.008%29=.008\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( ".512+.384+.096+.008 = 1.000 so the calculations should be good.<br><BR>\n" );
document.write( "ANSWERS:<BR>\n" );
document.write( "(a) exactly 2: 0.384<BR>\n" );
document.write( "(b) at least 1: 1-.008 = 0.992<BR>\n" );
document.write( "(c) at most 2: 1-.512 = 0.488<BR>\n" );
document.write( "(d) less than 1: 0.008<BR>\n" );
document.write( "(e) (see above)<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );