document.write( "Question 1198017: Question 1
\n" ); document.write( "-The 112 students sat for an examination.Question 1 was answered by 50 students,Question 2 by 66 students,Question 3 by 38 students.32 students attempeted Q2 and Q1,22 students attempted Q2&Q3,20 students attempted Q3&Q1,8 students attempted all the questions.How many students didn't attempt any questi\r
\n" ); document.write( "\n" ); document.write( "Question 2
\n" ); document.write( "Supposed 2 coins are tosed,events A and B are defined as follows; A is the event of getting a head in the first coin.B is the event that the coin falls alike.Fknd the probability of the event A happening given that B has happened and the probability of event B happening given that A has already happened.\r
\n" ); document.write( "\n" ); document.write( "Question 3
\n" ); document.write( "Past records shown that the probability of a school football twam winning a match is 0.7.How many possible games might the school win in 30 matches \n" ); document.write( "

Algebra.Com's Answer #831511 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Question 1
\n" ); document.write( "The 112 students sat for an examination.
\n" ); document.write( "Question 1 was answered by 50 students, Question 2 by 66 students, Question 3 by 38 students.
\n" ); document.write( "32 students attempeted Q2 and Q1, 22 students attempted Q2 and Q3, 20 students attempted Q3 Q1,
\n" ); document.write( "8 students attempted all the questions. How many students didn't attempt any questi
\n" ); document.write( "Question 2
\n" ); document.write( "Supposed 2 coins are tosed,events A and B are defined as follows; A is the event of getting a head in the first coin.
\n" ); document.write( "B is the event that the coin falls alike.Fknd the probability of the event A happening given that B has happened
\n" ); document.write( "and the probability of event B happening given that A has already happened.
\n" ); document.write( "Question 3
\n" ); document.write( "Past records shown that the probability of a school football twam winning a match is 0.7.
\n" ); document.write( "How many possible games might the school win in 30 matches
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " I will answer Q1 and Q3, only.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " Question 1\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Use the Inclusion-Exclusion principle (formula).  The number of those who attempted at least one of the questions is\r\n" );
document.write( "\r\n" );
document.write( "    n(Q1 U Q2 U Q3) = n(Q1) + n(Q2) + n(Q3) - n(Q1 and Q2) - n(Q1 and Q3) - n(Q2 and Q3) + n(Q1 and Q2 and Q3) = \r\n" );
document.write( "\r\n" );
document.write( "                    =  50   +  66   +  38   -     32       -     20       -     22       +          8          = 88.\r\n" );
document.write( "\r\n" );
document.write( "Thus the number of those who didn't attempt any question is the COPMPLEMENT of 88 to 112, i.e.  112 - 88 = 24.    ANSWER\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " Question 3\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "They ask about the mathematical expectation.  You may use your intuition (= common sense) or strict mathematical formula\r\n" );
document.write( "\r\n" );
document.write( "for the mathematical expectation of the binomial distribution with 30 trials and the probability of success p = 0.7 \r\n" );
document.write( "for each individual trial.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In any case, the ANSWER  is  this number  E = n*p = 0.7*30 = 21.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "On inclusion-exclusion principle, see this Wikipedia article\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "https://en.wikipedia.org/wiki/Inclusion%E2%80%93exclusion_principle\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "To see many other similar (and different) solved problems on Inclusion-Exclusion, see the lessons\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "    - Counting elements in sub-sets of a given finite set\r
\n" ); document.write( "\n" ); document.write( "    - Advanced problems on counting elements in sub-sets of a given finite set\r
\n" ); document.write( "\n" ); document.write( "    - Challenging problems on counting elements in subsets of a given finite set \r
\n" ); document.write( "\n" ); document.write( "    - Selected problems on counting elements in subsets of a given finite set \r
\n" ); document.write( "\n" ); document.write( "    - Inclusion-Exclusion principle problems \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Happy learning (!)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );