document.write( "Question 648024: \"A student has to sit for an examination consisting of 3 questions selected randomly from a list of 100 questions. To pass, he should answer all the three questions. What is the probability that the student will pass the examination, if he knows the answer to 90 questions on the list.\"\r
\n" ); document.write( "\n" ); document.write( "I have asked this question before and i got the answer as .729 but its the wrong answer. I have also solved it the same but correct answer is .798 and i don't know how to get this one...?????????
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #852483 by ikleyn(53603) $\"\"$ $\"About$

You can put this solution on YOUR website!
A student has to sit for an examination consisting of 3 questions selected randomly from a list of 100 questions.
\n" ); document.write( "To pass, he should answer all the three questions. What is the probability that the student will pass the examination,
\n" ); document.write( "if he knows the $\"highlight%28cross%28answer%29%29\"$ answers to 90 questions on the list.
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The problem can be solved in two ways.
\n" ); document.write( "I will present both the ways below.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "                   First, simple way\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The probability correctly answer 1st question is  .\r\n" );
document.write( "\r\n" );
document.write( "The probability correctly answer 2nd question is    (if the 1st is just answered correctly).\r\n" );
document.write( "\r\n" );
document.write( "The probability correctly answer 3rd question is    (if both the 1st and the 2nd questions are just answered correctly).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The probability to pass the exam is\r\n" );
document.write( "\r\n" );
document.write( "    P =  = 0.7265  (rounded).    <<<---===  ANSWER\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "         Second, slightly more complicated way\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The number of all triple questions taken from 100 questions is  C(100,3) = 161700 combinations.\r\n" );
document.write( "\r\n" );
document.write( "The number of all \"correct\" triples questions taken from 90 questions is  C(90,3) = 117480.\r\n" );
document.write( "\r\n" );
document.write( "The probability under the problem's question is the ratio\r\n" );
document.write( "\r\n" );
document.write( "    P =  =  = 0.7265  (rounded).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "You get the same answer.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Thus you have two solutions from my post for your better understanding.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );