document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=548982>Question 548982</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ten percent of the population is left handed. What is the probability that in a group of 10 people, at least two will be left handed? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #357385 by </B><A HREF=/tutors/aboutme.mpl?userid=mathie123><B>mathie123(224)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathie123><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=357385\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a binomial distribution with the P(win)=P(left-handed)=10% and P(fail)=P(right-handed)=90%.\r<BR>\n" );
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document.write( "We have a formula we can directly plug into the binomial distribution, but just so we know where it is coming from I will derive it. \r<BR>\n" );
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document.write( "P(at least 2 left handed)=1-P(0 left-handed)-P(1 left-handed)   <BR>\n" );
document.write( "(This takes a bit of thinking... basically everything must add to 100%, so I picked the shorter route and subtracted everything it CANNOT be... please let me know if you are unsure)\r<BR>\n" );
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document.write( "Let's first find P(0 lefthanded)<BR>\n" );
document.write( "Well this means out of the 10 people, 0 of them are \"winning\"(i.e. left-handed).  how many ways can I choose these 0 people?  10C0=1<BR>\n" );
document.write( "Okay so once I have the left-handed people picked out, the rest are just right-handed (10 people).  <BR>\n" );
document.write( "So the probability that 10 people are right-handed is 90%*90%*...90% (10 times- using product rule)=0.9^(10)<BR>\n" );
document.write( "and the probability that 0 people are left-handed is 0.1^0=1\r<BR>\n" );
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document.write( "So P(0 left-handed) using the product rule is <BR>\n" );
document.write( "(10C0)*(09^(10))*(0.1^0)<BR>\n" );
document.write( "I will let you figure this out on your calculator.... \r<BR>\n" );
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document.write( "We can do a similar thing for P (1 left-handed) and find that in general if we have a \"win/fail\" situation, and we want the probability that we have r wins out of a total of n trials, our formula will look like this:<BR>\n" );
document.write( "P(r wins)=(nCr)*(P(win))^r*(P(fail))^(n-r)\r<BR>\n" );
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document.write( "Try this out for P( 1 lefthanded) then put these two values we found into the <BR>\n" );
document.write( "P(at least 2 left handed)=1-P(0 left-handed)-P(1 left-handed)  <BR>\n" );
document.write( "formula we have\r<BR>\n" );
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document.write( "Hopefully this helps:) </SPAN>\n" );
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