document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171245>Question 1171245</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine if the events are unusual. If convenient, use the appropriate probability table or technology to find the probabilities.<BR>\n" );
document.write( "Fifty-three <BR>\n" );
document.write( "percent of adults say that they have cheated on a test or exam before. You randomly select <BR>\n" );
document.write( "seven <BR>\n" );
document.write( "adults. Find the probability that the number of adults who say that they have cheated on a test or exam before is (a) exactly <BR>\n" );
document.write( "four, <BR>\n" );
document.write( "(b) more than <BR>\n" );
document.write( "two, <BR>\n" );
document.write( "and (c) at most <BR>\n" );
document.write( "five.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #796179 by </B><A HREF=/tutors/aboutme.mpl?userid=Solver92311><B>Solver92311(821)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Solver92311><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=Solver92311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=796179\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "The probability of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large k\"> successes in <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\"> independent trials where the probability of success for any single trial is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large p\"> is given by:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P(k,n,p)\ =\ {{n}\choose{k}}\,\(p\)^k\(1\,-\,p\)^{n-k}\">\r<BR>\n" );
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document.write( "The probability of more than <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large k\"> successes is then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P(> k,n,p)\ =\ \sum_{r=k+1}^n\,{{n}\choose{r}}\,\(p\)^r\(1\,-\,p\)^{n-r}\">\r<BR>\n" );
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document.write( "Alternatively, it may save some arithmetic to note that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large P(> k,n,p)\ =\ 1\ -\ P(<=k,n,p)\ =\ 1\ - \sum_{0}^k\,{{n}\choose{r}}\,\(p\)^r\(1\,-\,p\)^{n-r}\">\r<BR>\n" );
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document.write( "\"At most\" means less than or equal which might be easier to calculate using one minus greater than.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=Solver92311&illustration_name=darwinfish.jpg\">\r<BR>\n" );
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document.write( "From <https://www.algebra.com/cgi-bin/upload-illustration.mpl> <BR>\n" );
document.write( "I > Ø<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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