document.write( "Question 1119912: Please help me solve this in simple way.\r
\n" ); document.write( "\n" ); document.write( "A quick quiz consists of 3 multiple choice problems, each of which has 5 answers, only one of which is correct. If you make random guesses on all 3 problems,
\n" ); document.write( "(a) What is the probability that all 3 of your answers are incorrect?\r
\n" ); document.write( "\n" ); document.write( "answer:
\n" ); document.write( "(b) What is the probability that all 3 of your answers are correct?\r
\n" ); document.write( "\n" ); document.write( "answer:
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #735559 by ikleyn(52798) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "A quick quiz consists of 3 multiple choice problems, each of which has 5 answers, only one of which is correct.
\n" ); document.write( "If you make random guesses on all 3 problems,\r
\n" ); document.write( "\n" ); document.write( "What is the probability that all 3 of your answers are incorrect ?
\n" ); document.write( "What is the probability that all 3 of your answers are correct ?\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "    Imagine that for each of the 3 multiple choice question the answers are labeled by 5 letters A, B, C, D and E  \r\n" );
document.write( "\r\n" );
document.write( "    (5 possible answers to each question).\r\n" );
document.write( "\r\n" );
document.write( "     By answering to each question, you mark your answer by one of the 5 letters.\r\n" );
document.write( "\r\n" );
document.write( "     So, by answering to 3 questions, you write the word of the length 3, using one of 5 letters in each of the three positions.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     It is your model. The entire space of events consists of all  = 125 such words of the length 3, written in 5-letter alphabet.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "         Now we are ready to answer the problem's questions.\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "(a) What is the probability that all 3 of your answers are incorrect ?\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "     If all 3 of your answers are incorrect, it means that in each of the 3 positions you put one of 4 letters, distinct of correct.\r\n" );
document.write( "\r\n" );
document.write( "     You can do it in   ways, therefore, the probability under the question is   =  =  = 0.512.\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "(b) What is the probability that all 3 of your answers are correct ?\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "     If all 3 of your answers are correct, it means that in each of the 3 positions you guessed the correct letter.\r\n" );
document.write( "\r\n" );
document.write( "     There is ONLY ONE way to do it; therefore, the probability under the question is   =  = 0.008.\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "All questions are answered.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The problem is solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );