document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1018955>Question 1018955</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A retail company must choose a few employees to send to a national retail conference. Of the 707 employees at this company, 504 are male. If 4 employees are randomly chosen, find the probability that exactly 3 are male. </SPAN>\n" );
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document.write( "Question:<BR>\n" );
document.write( "A retail company must choose a few employees to send to a national retail conference. Of the 707 employees at this company, 504 are male. If 4 employees are randomly chosen, find the probability that exactly 3 are male.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Solution:<BR>\n" );
document.write( "Choosing the first male is 504 out of 707.<BR>\n" );
document.write( "Choosing the second male is 503 out of 706.<BR>\n" );
document.write( "Choosing the third male is 502 out of 705.<BR>\n" );
document.write( "The probability of randomly choosing male for all three is therefore the product of each, according to the multiplication rule.<BR>\n" );
document.write( " <BR>\n" );
document.write( "P(3 males)<BR>\n" );
document.write( "=(504*503*502)/(707*706*705)<BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3030072%2F8378455 ALIGN=MIDDLE  ALT=\"3030072%2F8378455\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=0.362 (approximately)<BR>\n" );
document.write( " <BR>\n" );
document.write( "Alternatively, if you have done hypergeometric distribution, it would be applicable here.<BR>\n" );
document.write( "Let <BR>\n" );
document.write( "A=number of males, 504<BR>\n" );
document.write( "B=number of non-males, 707-504=203<BR>\n" );
document.write( "a=number of males chosen, 3<BR>\n" );
document.write( "b=number of non-males chosen, 0<BR>\n" );
document.write( "and<BR>\n" );
document.write( "C(n,r):=n!/(r!(n-r)!)  [combination of r objects out of n]<BR>\n" );
document.write( "P(a,b)=C(A,a)*C(B,b)/C(A+B,a+b)<BR>\n" );
document.write( "=><BR>\n" );
document.write( " <BR>\n" );
document.write( "P(3,0)=C(504,3)*C(203,0)/C(707,3)<BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3030072%2F8378455 ALIGN=MIDDLE  ALT=\"3030072%2F8378455\"   DISABLED_style= \"max-width:90%; height:auto;\" > as before.<BR>\n" );
document.write( "The advantage of using hypergeometric distribution is that it is a systematic method, requiring very little input.<BR>\n" );
document.write( "For example, the same problem but choosing 25 male candidates and 5 female candidates would be:<BR>\n" );
document.write( "P(25,5)=C(504,25)*C(203,5)/C(707,30)<BR>\n" );
document.write( "=0.057 (approximately) </SPAN>\n" );
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