document.write( "Question 1010051: Suppose a math class contains 33 students, 19 females (three of whom speak French) and 14 males (three of whom speak French). Compute the probability that a randomly selected student is female, given that the student speaks French. \n" ); document.write( "
Algebra.Com's Answer #625544 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
Question 1008795
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document.write( "We make this chart:\r\n" );
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document.write( "                | MALE |FEMALE|TOTALS|\r\n" );
document.write( "-------------------------------------|\r\n" );
document.write( "Speak French    |      |      |      |\r\n" );
document.write( "-------------------------------------|\r\n" );
document.write( "Don't speak it  |      |      |      |\r\n" );
document.write( "-------------------------------------|\r\n" );
document.write( "TOTALS          |      |      |      |\r\n" );
document.write( "-------------------------------------|\r\n" );
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\r
\n" ); document.write( "\n" ); document.write( ">>Suppose a math class contains 33 students,<< \r
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document.write( "So we put 33 in the lower right had corner under total.\r\n" );
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document.write( "                | MALE |FEMALE|TOTALS|\r\n" );
document.write( "-------------------------------------|\r\n" );
document.write( "Speak French    |      |      |      |\r\n" );
document.write( "-------------------------------------|\r\n" );
document.write( "Don't speak it  |      |      |      |\r\n" );
document.write( "-------------------------------------|\r\n" );
document.write( "TOTALS          |      |      |  33  |\r\n" );
document.write( "-------------------------------------|\r\n" );
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document.write( "

\n" ); document.write( " 19 females (three of whom speak French)
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document.write( "So we put 19 in the total females and 3 in the box\r\n" );
document.write( "under Females that speak French\r\n" );
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document.write( "                | MALE |FEMALE|TOTALS|\r\n" );
document.write( "-------------------------------------|\r\n" );
document.write( "Speak French    |      |   3  |      |\r\n" );
document.write( "-------------------------------------|\r\n" );
document.write( "Don't speak it  |      |      |      |\r\n" );
document.write( "-------------------------------------|\r\n" );
document.write( "TOTALS          |      |  19  |  33  |\r\n" );
document.write( "-------------------------------------|\r\n" );
document.write( "

\n" ); document.write( ">>and 14 males (three of whom speak French)<<
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document.write( "So we put 14 in the total males and 3 in the box\r\n" );
document.write( "under Males that speak French\r\n" );
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document.write( "                | MALE |FEMALE|TOTALS|\r\n" );
document.write( "-------------------------------------|\r\n" );
document.write( "Speak French    |   3  |   3  |      |\r\n" );
document.write( "-------------------------------------|\r\n" );
document.write( "Don't speak it  |      |      |      |\r\n" );
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document.write( "TOTALS          |  14  |  19  |  33  |\r\n" );
document.write( "-------------------------------------|\r\n" );
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document.write( "Now we can fill in the rest of the chart:\r\n" );
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document.write( "We add 3+3 and get 6 and put that in the upper right box for\r\n" );
document.write( "the total who speak French.\r\n" );
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document.write( "We subtract 14-3 = 11 and put for the Males who don't speak\r\n" );
document.write( "French.\r\n" );
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document.write( "We subtract 18-3 = 16 and put for the Females who don't speak\r\n" );
document.write( "French.\r\n" );
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document.write( "                | MALE |FEMALE|TOTALS| ***\r\n" );
document.write( "-------------------------------------|\r\n" );
document.write( "Speak French    |   3  |   3  |   6  |\r\n" );
document.write( "-------------------------------------|\r\n" );
document.write( "Don't speak it  |  11  |  16  |      |\r\n" );
document.write( "-------------------------------------|\r\n" );
document.write( "TOTALS          |  14  |  19  |  33  |\r\n" );
document.write( "-------------------------------------|\r\n" );
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document.write( "Now we fill in the total who don't speak French\r\n" );
document.write( "by either adding 11+16=27, or by subtracting 6\r\n" );
document.write( "who speak French from the 33 total, getting \r\n" );
document.write( "33=6=27.  This is a check that we've done everything\r\n" );
document.write( "correctly.\r\n" );
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document.write( "                | MALE |FEMALE|TOTALS|\r\n" );
document.write( "-------------------------------------|\r\n" );
document.write( "Speak French    |   3  |   3  |   6  |\r\n" );
document.write( "-------------------------------------|\r\n" );
document.write( "Don't speak it  |  11  |  16  |  27  |\r\n" );
document.write( "-------------------------------------|\r\n" );
document.write( "TOTALS          |  14  |  19  |  33  |\r\n" );
document.write( "-------------------------------------|\r\n" );
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document.write( "

\n" ); document.write( "Compute the probability that a randomly selected student
\n" ); document.write( "is female, given that the student speaks French.
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document.write( "Since we are given that the student speaks French we reduce\r\n" );
document.write( "the sample space to just the top row, eliminating all the\r\n" );
document.write( "ones who don't speak French:\r\n" );
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document.write( "                | MALE |FEMALE|TOTALS|\r\n" );
document.write( "-------------------------------------|\r\n" );
document.write( "Speak French    |   3  |   3  |   6  |\r\n" );
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document.write( "That's 3 out of 6 or \"3%2F6\" which reduces to \"1%2F2\".\r\n" );
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document.write( "Heck, we could have answered that up there where the 3 stars \r\n" );
document.write( "*** are.  We didn't need to even finish filling in the chart.\r\n" );
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document.write( "Edwin
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