document.write( "Question 1117492: A multiple-choice quiz has 15 questions, each with 4 possible answers of which only 1 is the correct answer. What is the probability that a student gets at least 1 correct answer? \n" ); document.write( "

Algebra.Com's Answer #732590 by ikleyn(52903) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "1.  The basic space of events has   elements.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    Each element of this set is the word of the length 15 with 4 possible letters/symbols in each of 15 positions.\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "    You can consider these letters as A, B, C and D, symbolizing the possible answer option on each of 15 questions.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    In other terms, the basic space of events is the set of the words of the length 15 over the alphabet consisting of 4 letters/symbols.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "2.  In each of 15 positions, there is only one \"correct\" symbol, symbolizing the correct answer.  \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    Other 3 symbols in each position correspond to incorrect answers.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    Thus the set of \"unwanted\" events has   elements.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    Each element is  15-letter word,  which has one of the three \"incorrect\" answers in each of the 15 position.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "3.  Therefore, the probability to have ALL incorrect answers to each of 15 questions is  \r\n" );
document.write( "\r\n" );
document.write( "     =  =  = 0.013363 . . . \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    while the probability to get at least 1 correct answer is  \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     -  =  =  = 1 - 0.013363 = 0.986637 . . . ,  or  98.66%.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Answer. The probability under the question is 0.9866, or 98/66%.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );