document.write( "Question 1172995: Suppose the probability of snow is 20%, and the probability of a traffic accident is 10%. Suppose further that the conditional probability of an accident, given that it snows, is 40%. What is the conditional probability that it snows, given that there is an accident? \n" ); document.write( "
Algebra.Com's Answer #798151 by ikleyn(52787)\"\" \"About 
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\n" ); document.write( "Suppose the probability of snow is 20%, and the probability of a traffic accident is 10%. Suppose further that
\n" ); document.write( "the conditional probability of an accident, given that it snows, is 40%. What is the conditional probability
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\n" ); document.write( "\n" ); document.write( "            It is a good question.\r
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document.write( "This problem relates, as you may conclude from the text, to conditional probability.\r\n" );
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document.write( "Let A be the event of snow.              Its probability is  20% = 0.2  (given).    (1)\r\n" );
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document.write( "Let B be the event of traffic accident.  Its probability is  10% = 0.1  (given).    (2)\r\n" );
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document.write( "The event of an accident, given that it snows, is the conditional probability  P(B|A).\r\n" );
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document.write( "This conditional probability  P(B|A)  is the ratio  P(B|A) = P(A ∩ B) / P(A).\r\n" );
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document.write( "Its value is given by the condition : it is  P(B|A) = 40% = 0.4.  So,  P(A ∩ B) / P(A) = 0.4.    (3)\r\n" );
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document.write( "Having  known (3) and (1), you can calculate  P(A ∩ B) = 0.4 * P(A) = 0.4 * 0.2 = 0.08.\r\n" );
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document.write( "        It is the key step in the solution:  from the given data we managed to determine that  P(A ∩ B) = 0.08.\r\n" );
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document.write( "        At this point, make a deep breath, and we will go further.\r\n" );
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document.write( "The problem asks us about OTHER conditional probability  P(B|A)  of the event  \"snows, given that there is an accident\".\r\n" );
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document.write( "This conditional probability is the ratio  P(B|A) = P(A ∩ B) / P(B).\r\n" );
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document.write( "We just know  P(A ∩ B), which is 0.08 (see (4) ). And we know P(B) = 0.1 (given)  (see (2) ).\r\n" );
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document.write( "THEREFORE,  P(B|A) = P(A ∩ B) / P(B) = \"0.08%2F0.1\" = 0.8.\r\n" );
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document.write( "The problem is just solved and you get the\r\n" );
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document.write( "ANSWER.  The conditional probability that it snows, given that there is an accident, is 0.8.\r\n" );
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\n" ); document.write( "\n" ); document.write( "The better solution and better explanation you will find NOWHERE.\r
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\n" ); document.write( "\n" ); document.write( "On conditional probability,  see my 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( "Read them to develop your skills and knowledge.\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( "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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