document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1107254>Question 1107254</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Two people are selected from a group of eight women and ten men. Find the probability that<BR>\n" );
document.write( "      a)   Both are men.<BR>\n" );
document.write( "      b)   At least one is a woman.<BR>\n" );
document.write( " </SPAN>\n" );
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document.write( "In both cases, you are choosing 2 out of the 18 people in the group, so the denominator of the probability fraction is \"18 choose 2\":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2818%2C2%29+=+%2818%2A17%29%2F%282%2A1%29+=+153 ALIGN=MIDDLE  ALT=\"C%2818%2C2%29+=+%2818%2A17%29%2F%282%2A1%29+=+153\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "a) If both are men, then you are choosing 2 of the 10 men and 0 of the 8 women.  The numerator of the probability fraction is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2810%2C2%29%2AC%288%2C0%29+=+45%2A1+=+45 ALIGN=MIDDLE  ALT=\"C%2810%2C2%29%2AC%288%2C0%29+=+45%2A1+=+45\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The probability that both are men is 45/153 = 9/17.<br><BR>\n" );
document.write( "b) \"at least one is a woman\" is the opposite (complement) of \"both are men\".  So the probability  that at least one is a woman is 1 - 9/17 = 8/17. </SPAN>\n" );
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