document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1111045>Question 1111045</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A doctor knows from experience that 18% of the patients to whom she gives a certain drug will have undesirable side effects. Among the 9 patients to whom she gives the drug, find the following probabilities. (Give your answers correct to three decimal places.)<BR>\n" );
document.write( "(a) Find the probability P(At most two will have undesirable side effects). <BR>\n" );
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document.write( "(b) Find the probability P(At least two will have undesirable side effects). <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 #726057 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=726057\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The probability of one patient having undesirable side effects is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2218%25%22=0.18 ALIGN=MIDDLE  ALT=\"%2218%25%22=0.18\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The probability of one patient not having undesirable side effects is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-0.18=0.82 ALIGN=MIDDLE  ALT=\"1-0.18=0.82\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "In a binomial distribution,<BR>\n" );
document.write( "the probabilities of exactly 0, 1, and 2 out of 9 patients having undesirable side effects<BR>\n" );
document.write( "would be the coefficients of the first three terms of<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.82%2B0.18s%29%5E9=0.82%5E9%2B9%2A0.82%5E8%2A0.18s%2B36%2A0.8%5E7%2A0.18%5E2s%5E2%2B%22...%22 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The first term is the probability of exactly 0 patients having undesirable side effects.<BR>\n" );
document.write( "Rounding, it is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.82%5E9=0.16762=%2216.762%25%22 ALIGN=MIDDLE  ALT=\"0.82%5E9=0.16762=%2216.762%25%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The second term represents the probability of exactly 1 patients having undesirable side effects.<BR>\n" );
document.write( "Rounding, its coefficient is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2A0.82%5E8%2A0.18=0.33115=%2233.115%25%22 ALIGN=MIDDLE  ALT=\"9%2A0.82%5E8%2A0.18=0.33115=%2233.115%25%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The third term represents the probability of exactly 2 patients having undesirable side effects.<BR>\n" );
document.write( "Rounding, its coefficient is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36%2A0.8%5E7%2A0.18%5E2=0.29077=%2229.077%25%22 ALIGN=MIDDLE  ALT=\"36%2A0.8%5E7%2A0.18%5E2=0.29077=%2229.077%25%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "(a) P(At most two will have undesirable side effects) =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.16762%2B0.33115%2B0.29077=0.78954=%2278.954%25%22 ALIGN=MIDDLE  ALT=\"0.16762%2B0.33115%2B0.29077=0.78954=%2278.954%25%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Presumably the teacher wants the probability as a decimal,<BR>\n" );
document.write( "and the answer \"correct to three decimal places\" would be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%220.790%22%29 ALIGN=MIDDLE  ALT=\"highlight%28%220.790%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "We can tell the doctor that<BR>\n" );
document.write( "P(At most two will have undesirable side effects) =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%2279.0%25%22%29 ALIGN=MIDDLE  ALT=\"highlight%28%2279.0%25%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "(b) P(Less than 2 patients having undesirable side effects)<BR>\n" );
document.write( "= P(no undesirable side effects) + P(exactly one patient having undesirable side effects)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22=%22 ALIGN=MIDDLE  ALT=\"%22=%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.16762%2B0.33115=0.49877 ALIGN=MIDDLE  ALT=\"0.16762%2B0.33115=0.49877\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The opposite of that is 2 or more patients having undesirable side effects,<BR>\n" );
document.write( "or \"at least two\" patients having undesirable side effects, so<BR>\n" );
document.write( "P(At least two will have undesirable side effects) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22=%22 ALIGN=MIDDLE  ALT=\"%22=%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-0.49877=0.50123 ALIGN=MIDDLE  ALT=\"1-0.49877=0.50123\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "the answer \"correct to three decimal places\" would be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%220.501%22%29 ALIGN=MIDDLE  ALT=\"highlight%28%220.501%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
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