document.write( "Question 1200654: 5. The prevalence of smoking among youth in a certain country is 18%. Suppose we select six individuals from the youth
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Algebra.Com's Answer #834835 by ikleyn(52847) $\"\"$ $\"About$

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\n" ); document.write( "The prevalence of smoking among youth in a certain country is 18%.
\n" ); document.write( "Suppose we select six individuals from the youth
\n" ); document.write( "What is the probability that at least one is a smoker?
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\n" ); document.write( "\n" ); document.write( "For this and many other similar problems, there is another way to solve,
\n" ); document.write( "which is much shorter and requires less calculations (and even less knowledge).\r
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document.write( "The problem asks about \"at least one person\".\r\n" );
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document.write( "    |  In such cases, the complement is \"no one person\",   |\r\n" );
document.write( "    |      so let's calculate the probability that         | \r\n" );
document.write( "    |         NO ONE of 6 individuals is a smoker.         |\r\n" );
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document.write( "It is  P =  = 0.3041   (rounded).\r\n" );
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document.write( "But we need the COMPLEMENTARY probability - - - so, our answer is  \r\n" );
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document.write( "    P' = 1 - 0.3041 = 0.6960  (rounded).\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "        Thus you may know nothing about the binomial distribution;
\n" ); document.write( "        you may know nothing about the relevant theory and formulas - nevertheless,
\n" ); document.write( "        your intuition and your common sense will lead you to the right answer.\r
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\n" ); document.write( "\n" ); document.write( "To see many other similar (and different) solved problems of this type, look into the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Solving probability problems using complementary probability \r
\n" ); document.write( "\n" ); document.write( "    - Solving probability problems using complementary probability REVISITED \r
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\n" ); document.write( "\n" ); document.write( "Every time, when you solve a Probability problem which asks about \" at least one \",
\n" ); document.write( "think about the complementary event \" No one \".\r
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\n" ); document.write( "\n" ); document.write( "As a rule, it is easier to calculate, and it gives you an easy and straightforward \r
\n" ); document.write( "\n" ); document.write( "way to get the answer. As a reward or a bonus, this way is, as a rule, more elegant.\r
\n" ); document.write( "\n" ); document.write( "So you earn additional scores in the eyes of other people - your friends, your classmates, \r
\n" ); document.write( "\n" ); document.write( "your teacher, your potential employer at the interview, or your students, if you are a teacher.\r
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\n" ); document.write( "\n" ); document.write( "Or even in the eyes of your children or grandchildren, if you teach them at home.\r
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\n" ); document.write( "\n" ); document.write( "        At the end, I think that I will not make a mistake if I say \r
\n" ); document.write( "\n" ); document.write( "        that this way is not only the DESIRED method of solution, \r
\n" ); document.write( "\n" ); document.write( "        but also is the EXPECTED way to solve this problem.\r
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