document.write( "Question 1163422: A man tossed two fair dice what is the conditional probability that the sum of the two
\n" ); document.write( "dice will be 7, given that [5]
\n" ); document.write( "(i) The sum is odd.
\n" ); document.write( "(ii) The sum is greater than 6.
\n" ); document.write( "(iii) The two dice had the same outcome.
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #787503 by ikleyn(52908)\"\" \"About 
You can put this solution on YOUR website!
.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Part   (i)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "The sample space is the set of all pairs (a,b), where \"a\" and \"b\" are integer numbers from 1 to 6 inclusive,\r\n" );
document.write( "representing possible outcomes tossing of two dice.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, the sample space has 6*6 = 36 elements, and they all have the same probability of  \"1%2F36\"  each.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now let's calculate the number of events with the odd sum of outcomes.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    2 elements have the sum 3 :  (1,2) and (2,1).\r\n" );
document.write( "\r\n" );
document.write( "    4 elements have the sum 5 :  (1,4), (2,3), (3,2) and (4,1).\r\n" );
document.write( "\r\n" );
document.write( "    6 elements have the sum 7 :  (1,6), (2,5), (3,4), (4,3), (5,2) and (6,1)\r\n" );
document.write( "\r\n" );
document.write( "    4 elements have the sum 9 :  (3,6), (4,5), (6,3) and (5,4)\r\n" );
document.write( "\r\n" );
document.write( "    2 elements have the sum 11:  (5,6) and (6,5).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The total number of events with the odd sum is  2 + 4 + 6 + 4 + 2 = 18.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Of them, the number of events with the sum 7 is 6.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Therefore, the conditional probability under the problem's question is  \"P%287%29%2FP%28odd%29\" = \"%28%286%2F36%29%29%2F%28%2818%2F36%29%29\" = \"6%2F18\" = \"1%2F3\".    ANSWER\r\n" );
document.write( "
\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Part (ii).   Do this part similarly.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Part   (iii)  is a good entertainment problem.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Its destination is to solve the problem  MENTALLY  and  MOMENTARILY  and to make a reader laughing.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The answer is:   the probability is zero,  since the number  7  is not the sum of two equal integer numbers.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-----------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If you want to learn this subject and this class of problems  BETTER,  DEEPER  and  WIDER,  look into the lesson\r
\n" ); document.write( "\n" ); document.write( "    - Rolling a pair of fair dice \r
\n" ); document.write( "\n" ); document.write( "in this site.  You will find there many other similar solved problems.\r
\n" ); document.write( "
\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
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic  \"Solved problems on Probability\". \r
\n" ); document.write( "
\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
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );