document.write( "Question 538727: Four dice are thrown. What is the probability that one of the rolls is a 6, given that one of the rolls is a 2? \n" ); document.write( "

Algebra.Com's Answer #353271 by AnlytcPhil(1810) $\"\"$ $\"About$

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Four dice are thrown. What is the probability that one of the rolls is a 6, given that one of the rolls is a 2?
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document.write( "This is a conditional probability   P(A|B) =  = \r\n" );
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document.write( "               number of rolls with both a 2 and a 6  \r\n" );
document.write( "Probability = --------------------------------------------\r\n" );
document.write( "                     number of rolls with a 6\r\n" );
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document.write( "We calculate the denominator first:\r\n" );
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document.write( "denominator =  =  - \r\n" );
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document.write( "denominator = 6×6×6×6 - 5×5×5×5 = 6⁴ - 5⁴ = 1296 - 625 = 671\r\n" );
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document.write( "numerator = \r\n" );
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document.write( "We use the formula \r\n" );
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document.write( "     N(A or B) = N(A) + N(B) - N(A and B) \r\n" );
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document.write( "Solving for N(A and B),\r\n" );
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document.write( "    N(A and B) = N(A) + N(B) - N(A or B)     \r\n" );
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document.write( "numerator =  =  +  - \r\n" );
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document.write( "We have already calculated  = 671\r\n" );
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document.write( "and\r\n" );
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document.write( " is the same quantity, that is, it is also 671\r\n" );
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document.write( "Now we only need to calculate \r\n" );
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document.write( " =  -  = 6⁴ - 4⁴ = 1296 - 256 = 1040\r\n" );
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document.write( "Now we go back to:\r\n" );
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document.write( "numerator =  =  +  -  = 671 + 671 - 1040 = 302.\r\n" );
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document.write( "Therefore the desired probability is .\r\n" );
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document.write( "Edwin

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