document.write( "Question 1201758: Two people are selected at random from a group of eight women and ten men. Find the probability of the following. (See Example 9. Round your answers to three decimal places.)
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Algebra.Com's Answer #836262 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Two people are selected at random from a group of eight women and ten men.
\n" ); document.write( "Find the probability of the following. (See Example 9. Round your answers to three decimal places.)
\n" ); document.write( "(a) both are men or both are women
\n" ); document.write( "(b) at least one is a woman
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document.write( "8 women + 10 men comprise 18 people, altogether.\r\n" );
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document.write( "Of 18 people, the number of different pairs of people is  \r\n" );
document.write( "       =  = 9*17 = 153.\r\n" );
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document.write( "Of 8 women, the the number of different pairs of women is  \r\n" );
document.write( "       =  = 4*7 = 28.\r\n" );
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document.write( "Of 10 men, the the number of different pairs of men is  \r\n" );
document.write( "       =  = 5*9 = 45.\r\n" );
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document.write( "So, the answer to question (a) is\r\n" );
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document.write( "    P =  =  = 0.477 (rounded).\r\n" );
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document.write( "To calculate the number of pairs, where at least one is woman, we subtract from 153\r\n" );
document.write( "the number of pairs (man,man), which is 45\r\n" );
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document.write( "    153-45 = 108.\r\n" );
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document.write( "To answer question (b), we relate this number of 108 to 153\r\n" );
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document.write( "    P =  = 0.706 (rounded).\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, with complete explanations.\r
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