document.write( "Question 1098933: If two fair dice are rolled, find the probability that the sum of the dice is 7, given that the sum is greater than 3. \n" ); document.write( "
Algebra.Com's Answer #713334 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "We start with the sample space of all 36 \r\n" );
document.write( "possible rolls:\r\n" );
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document.write( "(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)\r\n" );
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document.write( "(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)\r\n" );
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document.write( "(3,1) (3,2) (3,3) (3,4) (3,5) (3,6) \r\n" );
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document.write( "(4,1) (4,2) (4,3) (4,4) (4,5) (4,6) \r\n" );
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document.write( "(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)\r\n" );
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document.write( "(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)\r\n" );
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document.write( "The next step is to reduce the sample space by looking \r\n" );
document.write( "at what is given.  These words,starting with the word\r\n" );
document.write( "\"given\":\r\n" );
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\n" ); document.write( "given that the sum is greater than 3.
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document.write( "tell us to eliminate what is NOT given from the sample \r\n" );
document.write( "space, which is this reduced sample space which contains\r\n" );
document.write( "only those rolls whose sums are greater than 3:\r\n" );
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document.write( "            (1,3) (1,4) (1,5) (1,6)\r\n" );
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document.write( "      (2,2) (2,3) (2,4) (2,5) (2,6)\r\n" );
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document.write( "(3,1) (3,2) (3,3) (3,4) (3,5) (3,6) \r\n" );
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document.write( "(4,1) (4,2) (4,3) (4,4) (4,5) (4,6) \r\n" );
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document.write( "(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)\r\n" );
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document.write( "(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)\r\n" );
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document.write( "Now we have a reduced sample space which only\r\n" );
document.write( "has (count them!) 33 outcomes.\r\n" );
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document.write( "Now using that reduced sample space, we turn to\r\n" );
document.write( "the first part:
find the probability that the sum of the dice is 7
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document.write( "I will color those rolls with sum 7 red:\r\n" );
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document.write( "            (1,3) (1,4) (1,5) (1,6)\r\n" );
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document.write( "      (2,2) (2,3) (2,4) (2,5) (2,6)\r\n" );
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document.write( "(3,1) (3,2) (3,3) (3,4) (3,5) (3,6) \r\n" );
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document.write( "(4,1) (4,2) (4,3) (4,4) (4,5) (4,6) \r\n" );
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document.write( "(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)\r\n" );
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document.write( "(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)\r\n" );
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document.write( "Count the red ones.  There are 6.  That's 6 out of 33, or\r\n" );
document.write( "a probability of 6/33 which reduces to 2/11.\r\n" );
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document.write( "Edwin
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