document.write( "Question 1145654: 1.1 A fair die is rolled twice. Find the probability of the following events:
\n" ); document.write( "a. The second number is twice the first
\n" ); document.write( "b. The second number is not greater than the first
\n" ); document.write( "c. At least one number is greater than
\n" ); document.write( "3. 1.2 Two distinct diceAand Barerolled. Whatis the probabilityofeachofthe following events?
\n" ); document.write( " a. At least one 4 appears
\n" ); document.write( " b. Just one 4 appears
\n" ); document.write( " c. The sum of the face values is 7
\n" ); document.write( "d. One of the values is 3 and the sum of the two values is 5
\n" ); document.write( "e. One of the values is 3 or the sum of the two values is 5
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Algebra.Com's Answer #766888 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
1.1 A fair die is rolled twice. \r
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Here is the sample space of the 36 possible pairs of rolls:\r\n" );
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document.write( "(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)\r\n" );
document.write( " \r\n" );
document.write( "(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)\r\n" );
document.write( " \r\n" );
document.write( "(3,1) (3,2) (3,3) (3,4) (3,5) (3,6) \r\n" );
document.write( " \r\n" );
document.write( "(4,1) (4,2) (4,3) (4,4) (4,5) (4,6) \r\n" );
document.write( " \r\n" );
document.write( "(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)\r\n" );
document.write( " \r\n" );
document.write( "(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)\r\n" );
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a. The second number is twice the first \r
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I'll color those red  \r\n" );
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document.write( "(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)\r\n" );
document.write( " \r\n" );
document.write( "(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)\r\n" );
document.write( " \r\n" );
document.write( "(3,1) (3,2) (3,3) (3,4) (3,5) (3,6) \r\n" );
document.write( " \r\n" );
document.write( "(4,1) (4,2) (4,3) (4,4) (4,5) (4,6) \r\n" );
document.write( " \r\n" );
document.write( "(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)\r\n" );
document.write( " \r\n" );
document.write( "(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)\r\n" );
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document.write( "Count them.  There are 3.  The probability is 3 out of 36 or 3/36 \r\n" );
document.write( "which reduces to 1/12.\r\n" );
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b. The second number is not greater than the first \r
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I'll color those red:\r\n" );
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document.write( "(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)\r\n" );
document.write( " \r\n" );
document.write( "(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)\r\n" );
document.write( " \r\n" );
document.write( "(3,1) (3,2) (3,3) (3,4) (3,5) (3,6) \r\n" );
document.write( " \r\n" );
document.write( "(4,1) (4,2) (4,3) (4,4) (4,5) (4,6) \r\n" );
document.write( " \r\n" );
document.write( "(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)\r\n" );
document.write( " \r\n" );
document.write( "(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)\r\n" );
document.write( "\r\n" );
document.write( "Count them.  There are 21.  The probability is 21 out of 36 or 21/36 \r\n" );
document.write( "which reduces to 7/12.\r\n" );
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c. At least one number is greater than 3. \r
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I'll color those red:\r\n" );
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document.write( "(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)\r\n" );
document.write( " \r\n" );
document.write( "(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)\r\n" );
document.write( " \r\n" );
document.write( "(3,1) (3,2) (3,3) (3,4) (3,5) (3,6) \r\n" );
document.write( " \r\n" );
document.write( "(4,1) (4,2) (4,3) (4,4) (4,5) (4,6) \r\n" );
document.write( " \r\n" );
document.write( "(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)\r\n" );
document.write( " \r\n" );
document.write( "(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)\r\n" );
document.write( "\r\n" );
document.write( "Count them.  There are 27.  The probability is 27 out of 36 or 27/36 \r\n" );
document.write( "which reduces to 3/4.\r\n" );
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document.write( "
1.2 Two distinct dice A and B are rolled. \r
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That's the same as rolling one die twice. So the sample space is the same.\r\n" );
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document.write( "(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)\r\n" );
document.write( " \r\n" );
document.write( "(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)\r\n" );
document.write( " \r\n" );
document.write( "(3,1) (3,2) (3,3) (3,4) (3,5) (3,6) \r\n" );
document.write( " \r\n" );
document.write( "(4,1) (4,2) (4,3) (4,4) (4,5) (4,6) \r\n" );
document.write( " \r\n" );
document.write( "(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)\r\n" );
document.write( " \r\n" );
document.write( "(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)\r\n" );
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document.write( "
What is the probability of each of the following events?
\n" ); document.write( " a. At least one 4 appears\r
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I'll color those red.\r\n" );
document.write( "\r\n" );
document.write( "(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)\r\n" );
document.write( " \r\n" );
document.write( "(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)\r\n" );
document.write( " \r\n" );
document.write( "(3,1) (3,2) (3,3) (3,4) (3,5) (3,6) \r\n" );
document.write( " \r\n" );
document.write( "(4,1) (4,2) (4,3) (4,4) (4,5) (4,6) \r\n" );
document.write( " \r\n" );
document.write( "(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)\r\n" );
document.write( " \r\n" );
document.write( "(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)\r\n" );
document.write( "\r\n" );
document.write( "Count them.  There are 11.  The probability is 11 out of 36 or 11/36 \r\n" );
document.write( "which does not reduce.\r\n" );
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b. Just one 4 appears\r
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I'll color those red:\r\n" );
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document.write( "(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)\r\n" );
document.write( " \r\n" );
document.write( "(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)\r\n" );
document.write( " \r\n" );
document.write( "(3,1) (3,2) (3,3) (3,4) (3,5) (3,6) \r\n" );
document.write( " \r\n" );
document.write( "(4,1) (4,2) (4,3) (4,4) (4,5) (4,6) \r\n" );
document.write( " \r\n" );
document.write( "(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)\r\n" );
document.write( " \r\n" );
document.write( "(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)\r\n" );
document.write( "\r\n" );
document.write( "Count them.  There are 10.  The probability is 10 out of 36 or 10/36 \r\n" );
document.write( "which reduces to 5/18.\r\n" );
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document.write( "
c. The sum of the face values is 7\r
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I'll color those red:\r\n" );
document.write( "\r\n" );
document.write( "(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)\r\n" );
document.write( " \r\n" );
document.write( "(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)\r\n" );
document.write( " \r\n" );
document.write( "(3,1) (3,2) (3,3) (3,4) (3,5) (3,6) \r\n" );
document.write( " \r\n" );
document.write( "(4,1) (4,2) (4,3) (4,4) (4,5) (4,6) \r\n" );
document.write( " \r\n" );
document.write( "(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)\r\n" );
document.write( " \r\n" );
document.write( "(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)\r\n" );
document.write( "\r\n" );
document.write( "Count them.  There are 6.  The probability is 6 out of 36 or 6/36 \r\n" );
document.write( "which reduces to 1/6.\r\n" );
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document.write( "
d. One of the values is 3 and the sum of the two values is 5.\r
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I'll color those red:\r\n" );
document.write( "\r\n" );
document.write( "(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)\r\n" );
document.write( " \r\n" );
document.write( "(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)\r\n" );
document.write( " \r\n" );
document.write( "(3,1) (3,2) (3,3) (3,4) (3,5) (3,6) \r\n" );
document.write( " \r\n" );
document.write( "(4,1) (4,2) (4,3) (4,4) (4,5) (4,6) \r\n" );
document.write( " \r\n" );
document.write( "(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)\r\n" );
document.write( " \r\n" );
document.write( "(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)\r\n" );
document.write( "\r\n" );
document.write( "Count them.  There are 2.  The probability is 2 out of 36 or 1/18 \r\n" );
document.write( "which reduces to 1/12.\r\n" );
document.write( "\r\n" );
document.write( "
e. One of the values is 3 or the sum of the two values is 5\r
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I'll color those red.\r\n" );
document.write( "\r\n" );
document.write( "(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)\r\n" );
document.write( " \r\n" );
document.write( "(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)\r\n" );
document.write( " \r\n" );
document.write( "(3,1) (3,2) (3,3) (3,4) (3,5) (3,6) \r\n" );
document.write( " \r\n" );
document.write( "(4,1) (4,2) (4,3) (4,4) (4,5) (4,6) \r\n" );
document.write( " \r\n" );
document.write( "(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)\r\n" );
document.write( " \r\n" );
document.write( "(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)\r\n" );
document.write( "\r\n" );
document.write( "Count them.  There are 13.  The probability is 13 out of 36 or 13/36 \r\n" );
document.write( "which does not reduce.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
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