document.write( "Question 1189075: In a raffle, 1800 tickets are sold. 3 prizes will be given starting with 3rd prize, then second, then first. A person buys 16 tickets which are all eligible to win prizes. What are the odds of this person winning the top two prizes? \n" ); document.write( "

Algebra.Com's Answer #820336 by ikleyn(52855) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "In a raffle, 1800 tickets are sold. 3 prizes will be given starting with 3rd prize, then second, then first.
\n" ); document.write( "A person buys 16 tickets which are all eligible to win prizes.
\n" ); document.write( "What are the odds of this person winning the top two prizes?
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\n" ); document.write( "\n" ); document.write( " With this problem/post, I am in difficult position :\r
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document.write( "First of all, the problem is posed INCORRECTLY.\r\n" );
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document.write( "(1)  A standard lottery does not work in a way described in the post.\r\n" );
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document.write( "     A standard lottery HAS NO priority in the order of winning prizes. \r\n" );
document.write( "     The prize is won, if the number on the ticket coincides with the number given to the prize by the lottery machine.\r\n" );
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document.write( "     If the specific lottery works differently (as worded in the post), it must be thoroughly / carefully reflected \r\n" );
document.write( "     in the description, which is not done in the post.\r\n" );
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document.write( "(2)  The question is posed in a way, which makes it unclear.\r\n" );
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document.write( "     What is \"winning the top two prizes\" ? - - - Are they the 1st and the 2nd, only ?\r\n" );
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document.write( "     Or the 3rd and the 2nd, only ? - - - Or any two of the top three prizes ?\r\n" );
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document.write( "(3)  How the problem is worded, it makes it clear, that the problem formulation is not professional \r\n" );
document.write( "     and is ambiguous.\r\n" );
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document.write( "     It means that the problem came not from a peer-reviewed textbook: it is created by an unprofessional amateur,\r\n" );
document.write( "     or recovered from an UNTRUSTED source.\r\n" );
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document.write( "(4)  Regarding such posts, my position is that they do not deserve a professional consideration, AS A RULE.\r\n" );
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document.write( "     My position is that at this forum we, the tutors, teach the students / (the visitors) to solve correctly\r\n" );
document.write( "     posed mathematical problem, but we do not teach unprofessional \"problems' composers\" to create their \r\n" );
document.write( "     problems. These two activities (teaching to solve and teaching to create Math problems) are two\r\n" );
document.write( "     absolutely distinct areas with zero intersection. \r\n" );
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document.write( "     Similar as in music performing and composing are two distinct activities, requiring different skills.\r\n" );
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document.write( "     (4b) There are exclusions from this my rule. One possible exclusion is when the problem is outstandingly \r\n" );
document.write( "          nice (at least, potentially) or the solution is outstandingly educative (at least, potentially).\r\n" );
document.write( "          But this problem is a standard; it is difficult to consider it as outstanding.\r\n" );
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document.write( "(5)  Therefore, my standard position relating to such posts is EITHER ignore them, or EXPLAIN to the visitor\r\n" );
document.write( "     that it is posed incorrectly, or TO DELETE such post/(posts) to avoid unnecessary and unproductive \r\n" );
document.write( "     explanations/discussions.\r\n" );
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document.write( "     So, my choice was between ignoring, explaining or deleting . . . \r\n" );
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document.write( "(6)  But this case now became special. It became special  because the other tutor before me published INCORRECT SOLUTION.\r\n" );
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document.write( "     Now my concern is not about the visitor, who posted the problem (everything is clear to me about him . . . )\r\n" );
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document.write( "     My concern is about those future readers and next generations of students, who (probably) will read these \r\n" );
document.write( "     related solutions from the archive.\r\n" );
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document.write( "     They should be confident that the tutors of this forum (as an entire body) are able to read, to solve and to understand \r\n" );
document.write( "     the problems correctly and to interpret them adequately.\r\n" );
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document.write( "                   |    It is WHY I WRITE THESE LINES.     |\r\n" );
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document.write( "(7)  So, I will consider the problem in this REFORMULATED form\r\n" );
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document.write( "              In a raffle, 1800 tickets are sold. 2 prizes will be given, the 1st and the 2nd. \r\n" );
document.write( "              A person buys 16 tickets. What are the odds of this person winning the top two prizes?\r\n" );
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document.write( "     As I explained above, it is not the only possible interpretation of the problem.\r\n" );
document.write( "     Another interpretations are possible.\r\n" );
document.write( "     But I chose this one BECAUSE the other tutor solved it incorrectly in this formulation.\r\n" );
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document.write( "                     So, see my correct solution below.\r\n" );
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document.write( "(8)  The probability to win two prizes, having 16 tickets bought, is\r\n" );
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document.write( "        P =  = reduce fractions =  =  = .\r\n" );
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document.write( "     It means that the odds of this person in favor of winning the top two prizes  are  2 against 26985-2 = 26983.\r\n" );
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document.write( "ANSWER.  The odds of this person in favor of winning the top two prizes  are  2 against 26983.\r\n" );
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