document.write( "Question 1163654: A coin is tossed 3 times. define the events A and B as:
\n" ); document.write( "A = {num heads > num tails}
\n" ); document.write( "B = {1st toss is a head}
\n" ); document.write( "Find P(A|B) \n" ); document.write( "

Algebra.Com's Answer #787815 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "A coin is tossed 3 times. define the events A and B as:
\n" ); document.write( "A = {num heads > num tails}
\n" ); document.write( "B = {1st toss is a head}
\n" ); document.write( "Find P(A|B)
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document.write( "Let's write H for head and T for tail.\r\n" );
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document.write( "Then any outcome of 3 tosses can be written as a word of the length 3 written in this 2-letter alphabet,\r\n" );
document.write( "consisting of letters H an T.\r\n" );
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document.write( "In all, there are 8 possible outcomes.  They all are listed as such words in the list below\r\n" );
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document.write( "1)   H H H     (*)    (**)   (***)\r\n" );
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document.write( "2)   H H T     (*)    (**)   (***)\r\n" );
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document.write( "3)   H T H     (*)    (**)   (***)\r\n" );
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document.write( "4)   H T T     (*)\r\n" );
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document.write( "5)   T H H            (**)\r\n" );
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document.write( "6)   T H T\r\n" );
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document.write( "7)   T T H\r\n" );
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document.write( "8)   T T T \r\n" );
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document.write( "Notice that these outcomes have equal probability of   =   each.\r\n" );
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document.write( "By symbol (*), I marked that events where the 1st toss is a head.\r\n" );
document.write( "There are 4 such events,  nn 1), 2), 3) an 4).\r\n" );
document.write( "It is the set of events B.\r\n" );
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document.write( "By symbol (**), I marked that events where number of heads > number of tails.\r\n" );
document.write( "There are 4 such events,  nn 1), 2), 3) an 5).\r\n" );
document.write( "It is the set of events A.\r\n" );
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document.write( "By the definition of the conditional probability,\r\n" );
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document.write( "    P(A | B)  = P (A ∩ B) / P(B).\r\n" );
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document.write( "The intersection  (A ∩ B)  consists of three events  nn 1), 2) and 3)  in the list;  they are marked by the symbol (***).\r\n" );
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document.write( "Now,  P (A ∩ B) = ;  P(B) = ;  therefore,\r\n" );
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document.write( "      P(A | B)  =   = .\r\n" );
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document.write( "ANSWER.  P(A | B) = .\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, explained and completed.\r
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\n" ); document.write( "\n" ); document.write( "The conception of conditional probability is not a simple conception, and a student should work diligently
\n" ); document.write( "to understand it clearly. For it, it is normal to consult/to learn from several sources.\r
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\n" ); document.write( "\n" ); document.write( "If you want to learn more about the conditional probability, look into 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( "You will find there many other similar solved problems to learn from.\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
\n" ); document.write( "
\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( "Do not forget to post your \"THANKS\" for my teaching.\r
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