document.write( "Question 1195707: An urn contains 2 one-dollar bills, 1 five-dollar bill and 1 ten-dollar bill. A player draws bills one at a time without replacement from the urn until a ten-dollar bill is drawn. Then the game stops. All bills are kept by the player. Determine:\r
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Algebra.Com's Answer #828171 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "An urn contains 2 one-dollar bills, 1 five-dollar bill and 1 ten-dollar bill.
\n" ); document.write( "A player draws bills one at a time without replacement from the urn
\n" ); document.write( "until a ten-dollar bill is drawn. Then the game stops.
\n" ); document.write( "All bills are kept by the player. Determine:
\n" ); document.write( "(A) The probability of winning $16.
\n" ); document.write( "(B) The probability of winning all bills in the urn.
\n" ); document.write( "(C) The probability of the game stopping at the second draw.
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\n" ); document.write( "\n" ); document.write( " In this post, I will solve part (A), only - - - \r
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\n" ); document.write( "\n" ); document.write( " - - - in order for do not transform this nice problem into a mess.\r
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document.write( "(A)  Winning $16 may happen only for these sequences of drawn dollars, step by step\r\n" );
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document.write( "         (1,5,10) (with two possible instances for $1);\r\n" );
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document.write( "         (5,1,10) (with two possible instances for $1).\r\n" );
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document.write( "     Indeed, $10 must be drawn last, and the first and the second draws must be 1 and 5 in any order.\r\n" );
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document.write( "     So, for winning $16, there are only these 4 winning sequences/outcomes.\r\n" );
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document.write( "     From the other hand side, having $10 as the last drawing allows these sequences\r\n" );
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document.write( "        (10);  (1,10) (two instances, regarding two possible bills of $1);  (5,10);  \r\n" );
document.write( "        \r\n" );
document.write( "        (1,1,10) (two instances, regarding two possible permutations of the two $1 bills);\r\n" );
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document.write( "                 (1,5,10) (two instances);  (5,1,10)  (two instances);  (1,5,1,10)  (two instances, regarding two possible permutations of the two $1 bills);;\r\n" );
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document.write( "        (x,y,z,10), where x,y,z are 6 possible permutation of 3 bills $1, $1, and $5.\r\n" );
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document.write( "     So, in all in the game, there are 1 + 2 + 1 + 2 + 2 + 2 + 2 + 6 = 18 possible outcome sequences;\r\n" );
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document.write( "     of them, only 4 sequences are winning $16.\r\n" );
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document.write( "     Thus the probability under question (A) is   = .    ANSWER \r\n" );
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