document.write( "Question 1132192: A pair of dice is rolled together till a sum of either 5 or 7 is obtained. Then probability that 5 comes before 7 \n" ); document.write( "

Algebra.Com's Answer #749148 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "P(5) = 4/36 = 1/9
\n" ); document.write( "P(7) = 6/36 = 1/6
\n" ); document.write( "P(neither 5 nor 7) = 26/36 = 13/18

\n" ); document.write( "P(5 before 7) =
\n" ); document.write( "P((5 on first flip) OR
\n" ); document.write( " (neither 5 nor 7 on first flip AND 5 on second flip) OR
\n" ); document.write( " (neither 5 nor 7 on first flip AND neither 5 nor 7 on second flip AND 5 on third flip) OR
\n" ); document.write( "...) =

\n" ); document.write( "1/9 + (13/18)(1/9) + (13/18)(13/18)(1/9) + ...

\n" ); document.write( "This is an infinite geometric series with first term a = 1/9 and common ratio r = 13/18.

\n" ); document.write( "The formula for the sum of an infinite geometric series with first term a and common ratio r (|r|<1) is

\n" ); document.write( " $\"S+=+a%2F%281-r%29\"$

\n" ); document.write( "You can do the calculation. \n" ); document.write( "

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