document.write( "Question 103841: Here is the titanic data we are working with...\r
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\n" ); document.write( "female 126 344 470
\n" ); document.write( "male 1364 366 1730
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\n" ); document.write( "\n" ); document.write( "We are asked to show why the general addition rule is true and the hint was to use Venn Diagrams.
\n" ); document.write( "I have done P(A or B) = p(A) + p(B) - P (A and B)
\n" ); document.write( ".21+.73-.32=.62 but I don't understand \"how to show that the General Addition Rule is True\"?\r
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\n" ); document.write( "\n" ); document.write( "Jessica \n" ); document.write( "
Algebra.Com's Answer #75517 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
Solution by Edwin:
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document.write( "Here is the titanic data we are working with... \r\n" );
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document.write( "         died | survived | totals\r\n" );
document.write( "female|   126 |    344   |  470\r\n" );
document.write( " male |  1364 |    366   | 1730\r\n" );
document.write( "totals|  1490 |    710   | 2200 \r\n" );
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document.write( "We are asked to show why the general addition rule \r\n" );
document.write( "is true and the hint was to use Venn Diagrams.\r\n" );
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document.write( "Draw a rectangle on the left for all the Males\r\n" );
document.write( "and label it M:\r\n" );
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document.write( "To the right of that, draw a rectangle for all the\r\n" );
document.write( "Females and label it F:\r\n" );
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document.write( "Now draw a circle in the middle for the survivors\r\n" );
document.write( "and label it S\r\n" );
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document.write( "The left half of the circle contains the male\r\n" );
document.write( "survivors, so put 366 in the left half of the\r\n" );
document.write( "circle:\r\n" );
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document.write( "The males who died are in the left rectangle\r\n" );
document.write( "but outside the circle. So put 1364 there:\r\n" );
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document.write( "The right half of the circle contains the female\r\n" );
document.write( "survivors, so put 344 in the right half of the\r\n" );
document.write( "circle:\r\n" );
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document.write( "The females who died are in the right rectangle\r\n" );
document.write( "but outside the circle. So put 126 there:\r\n" );
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document.write( "Now to get P(M or S), we just look at this\r\n" );
document.write( "part of the Venn diagram:\r\n" );
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document.write( "So the number in this part is 1364+366+344 = 2074\r\n" );
document.write( "and since there were 2200 people on board, the\r\n" );
document.write( "probablity that a person on board was either male\r\n" );
document.write( "or survived is given by\r\n" );
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document.write( "P(M or S) = \"2074%2F2200\" = \"1037%2F1100\" \r\n" );
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document.write( "Now let's use the formula and see if we get the same answer:\r\n" );
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document.write( "P(M or S) = P(M) + P(S) - P(M and S)\r\n" );
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document.write( "P(M or S) = \"1730%2F2200\" + \"710%2F2200\" - \"366%2F2200\"\r\n" );
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document.write( "P(M or S} = \"%281730%2B710-366%29%2F2200\" = \"2074%2F2200\" = \"1037%2F1100\"\r\n" );
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document.write( "So we see that the general sum formula does agree \r\n" );
document.write( "with the Venn diagram answer.\r\n" );
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document.write( "We can also do the same thing with P(F or S)\r\n" );
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document.write( "Now to get P(F or S), we just look at this\r\n" );
document.write( "part of the Venn diagram:\r\n" );
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document.write( "So the number in this part is 366+344+126 = 836\r\n" );
document.write( "and since there were 2200 people on board, the\r\n" );
document.write( "probablity that a person on board was either female\r\n" );
document.write( "or survived is given by\r\n" );
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document.write( "P(F or S) = \"836%2F2200\" = \"19%2F50\" \r\n" );
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document.write( "Now let's use the formula and see if we get the same answer:\r\n" );
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document.write( "P(F or S) = P(F) + P(S) - P(F and S)\r\n" );
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document.write( "P(F or S) = \"470%2F2200\" + \"710%2F2200\" - \"344%2F2200\"\r\n" );
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document.write( "P(F or S} = \"%28470%2B710-344%29%2F2200\" = \"836%2F2200\" = \"19%2F50\"\r\n" );
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document.write( "So we see again that the general sum formula \r\n" );
document.write( "does agree with the Venn diagram answer.\r\n" );
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document.write( "Edwin
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