document.write( "Question 1163270: In a high school class of 100 students, 42 studied mathematics, 68 studied
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\n" ); document.write( "studied both mathematics and psychology, 7 studied history and neither
\n" ); document.write( "mathematics nor psychology, 10 studied all three subjects and 8 did not take
\n" ); document.write( "any of the three. If a student is selected at random, find the probability that
\n" ); document.write( " (i) he takes history and psychology but not mathematics?
\n" ); document.write( " (ii) a person enrolled in history takes all three subjects?
\n" ); document.write( " (iii) he takes mathematics only? \n" ); document.write( "

Algebra.Com's Answer #787310 by ikleyn(52813) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " In my response, I will solve/explain part (ii) ONLY.\r
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document.write( "(ii)   If a student is selected at random, find the probability that a person enrolled in history takes all three subjects?\r\n" );
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document.write( "       You are given that 54 study History and 10 study all three subjects.\r\n" );
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document.write( "       Therefore the probability under the question in this part is the ratio\r\n" );
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document.write( "                 P =  = .      ANSWER\r\n" );
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document.write( "       In this case, you can consider the set of the 54 who study History as the sample set of events (\"reduced sample set\") \r\n" );
document.write( "       and the set of the 10 who study all three subjects as the favorable set,\r\n" );
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document.write( "       so the probability    P = .\r\n" );
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\n" ); document.write( "\n" ); document.write( "This problem (ii) is a typical conditional probability problem.\r
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\n" ); document.write( "\n" ); document.write( "In such problems, the reduction of the sample set is one of the two STANDARD methods of solution. \r
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\n" ); document.write( "\n" ); document.write( "On conditional probability problems, see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Conditional probability problems \r
\n" ); document.write( "\n" ); document.write( "    - Conditional probability problems REVISITED \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Solved problems on Probability\"
\n" ); document.write( "and \"Additional problems on Probability\". \r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
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\n" ); document.write( "\n" ); document.write( "I do not like very much when the post goes with many (more than one) problems/questions.\r
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\n" ); document.write( "\n" ); document.write( "Then the answer EITHER becomes a mess OR is so short that prevents learning.\r
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\n" ); document.write( "\n" ); document.write( "Therefore, if you REALLY want to LEARN from this forum (and from me personally),
\n" ); document.write( "do not load many questions in your post.\r
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\n" ); document.write( "\n" ); document.write( "There is a brilliant method for solving part (i), so if you want to learn it from me,
\n" ); document.write( "re-post the problem again with the question (i) ONLY.\r
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\n" ); document.write( "\n" ); document.write( "Happy learning (!)\r
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\n" ); document.write( "\n" ); document.write( "By the way, the rules and the policy of this forum require directly, explicitly and formally
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