document.write( "Question 1146892: The finance department of a particular company has 15 employees, 6 of whom have MBA degrees. Suppose we select three different employees sequentially at random from this department. Determine the probability of the following events.\r
\n" ); document.write( "\n" ); document.write( "a) The first employee has an MBA, given that there is a total of one MBA among all three employees.
\n" ); document.write( "b) There are exactly two employees with an MBA, given that the first employee has an MBA.
\n" ); document.write( "c) The first employee has an MBA, given that there is at least one MBA among all three employees. \n" ); document.write( "
Algebra.Com's Answer #786218 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Here are the 8 cases and their enumerations. (let M indicate that an MBA is\r\n" );
document.write( "selected and N indicate that a Non-MBA is selected.\r\n" );
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document.write( "                                    The      Is the first  Are there    At  \r\n" );
document.write( "                                   exact       selected    exactly 2  least\r\n" );
document.write( "                                no. of MBAs     an MBA?     MBA's?    1 MBA?\r\n" );
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document.write( "#1  n(M M M) = (6)(5)(4) = 120       3           yes         no        yes \r\n" );
document.write( "#2  n(M M N) = (6)(5)(9) = 270       2           yes        yes        yes\r\n" );
document.write( "#3  n(M N M) = (6)(9)(5) = 270       2           yes        yes        yes\r\n" );
document.write( "#4  n(M N N) = (6)(9)(8) = 432       1           yes         no        yes\r\n" );
document.write( "#5  n(N M M) = (9)(6)(5) = 270       2            no        yes        yes\r\n" );
document.write( "#6  n(N M N) = (9)(6)(8) = 432       1            no         no        yes\r\n" );
document.write( "#7  n(N N M) = (9)(8)(6) = 432       1            no         no        yes\r\n" );
document.write( "#8  n(N N N) = (9)(8)(7) = 504       0            no         no         no\r\n" );
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document.write( "        15P3 = 15∙14∙13 = 2730   <--added as a check
a) The first employee has an MBA, given that there is a total of one MBA
\n" ); document.write( "among all three employees.
n(#4)/n(#4 or #6 or #7) = 432/(432+432+432) = 1/3
b) There are exactly two employees with an MBA, given that the first
\n" ); document.write( "employee has an MBA.
n(#2 or #3)/n(#1 or #2 or #3 or #4) = (270+270)/(120+270+270+432) = 540/1092\r\n" );
document.write( "= 45/91
c) The first employee has an MBA, given that there is at least one MBA among
\n" ); document.write( "all three employees.
n(#1 or #2 or #3 or #4)/n(#1 or #2 or #3 or #4 or #5 or #6 or #7) = \r\n" );
document.write( "(120+270+270+432)/(2730-504) = 1092/2226 = 26/53\r\n" );
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document.write( "Edwin
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