document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1023484>Question 1023484</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 8% of students are left handed. If 50 (FIFTY) classes of 20 (TWENTY) students are randomly selected, what is the probability that 10 <BR>\n" );
document.write( "(TEN) classes have no left-handed students?  </SPAN>\n" );
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document.write( "Question:8% of students are left handed. If 50 (FIFTY) classes of 20 (TWENTY) students are randomly selected, what is the probability that 10 <BR>\n" );
document.write( "(TEN) classes have no left-handed students? <BR>\n" );
document.write( " <BR>\n" );
document.write( "Solution:<BR>\n" );
document.write( "This question can be broken down into two steps.<BR>\n" );
document.write( "The first step is to apply the multiplication rule to find the probability of a class of 20 right-handed students.<BR>\n" );
document.write( "We need to assume that the students (and classes) are chosen randomly and independent of each other.<BR>\n" );
document.write( "Probability of success, i.e. 20 right-handed students, is obtained from the probability of randomly choosing a single right-handed student, equal to p=1-0.08=0.92. probability of a right-handed class will therefore be p^20, by the multiplication rule, where p^20=0.92^20=0.18869.<BR>\n" );
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document.write( "Now we have 50 classes, either right-handed or mixed.  To find the probability of (exactly) 10 classes out of the 50 are right-handed can be obtained by the binomial distribution, namely<BR>\n" );
document.write( "P(k;n;p)=C(n,k)*p^k*(1-p)^(n-k)<BR>\n" );
document.write( "where C(n,k) is the binomial coefficient = n!/(k!(n-k)!)<BR>\n" );
document.write( "p=probability of success (right-handed class)<BR>\n" );
document.write( "(1-p)=probability of failure (mixed class), and<BR>\n" );
document.write( "k=number of successes.<BR>\n" );
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document.write( "Applying the formula, we have<BR>\n" );
document.write( "P(10;50;0.18869)=C(50,10)*0.18869^10*(0.81131)^40<BR>\n" );
document.write( "=10272278170*5.72223*10^(-8)*2.33025*10^(-4)<BR>\n" );
document.write( "=0.13697 </SPAN>\n" );
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