document.write( "Question 919688: (a)From a stack of 3 dice, one is taken and rolled twice.
\n" ); document.write( "If, unknown to the gambler, two of the dice are weighted and each have a 1/7 chance of rolling a 6, what is the probability that the gambler rolls two 6's?
\n" ); document.write( "(b)If the gambler has rolled two sixes, what is the probability that he has rolled the weighted die?\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Need help solving this. Thanks in advance. \n" ); document.write( "

Algebra.Com's Answer #558287 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "(a)\r\n" );
document.write( "For him to roll 2 6's, he will \r\n" );
document.write( "\r\n" );
document.write( "EITHER\r\n" );
document.write( "\r\n" );
document.write( "1. choose a weighted die    <--probability = 2/3\r\n" );
document.write( "AND\r\n" );
document.write( "2. roll a 6 the first time  <--probability = 1/7\r\n" );
document.write( "AND\r\n" );
document.write( "3. roll a 6 the second time <--probability = 1/7\r\n" );
document.write( "\r\n" );
document.write( "OR\r\n" );
document.write( "\r\n" );
document.write( "1. choose a non-weighted die  <--probability = 1/3\r\n" );
document.write( "AND\r\n" );
document.write( "2. roll a 6 the first time  <--probability = 1/6\r\n" );
document.write( "AND\r\n" );
document.write( "3. roll a 6 the second time <--probability = 1/6\r\n" );
document.write( "\r\n" );
document.write( "AND suggests multiplication and OR suggests addition:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Approximately 0.023 \r\n" );
document.write( "\r\n" );
document.write( "---------\r\n" );
document.write( " (b)\r\n" );
document.write( "\r\n" );
document.write( "                                  P(weighted and (6 and 6) )\r\n" );
document.write( "P(weighted die | rolled 2 6's) = ------------------------\r\n" );
document.write( "                                      P(6 and 6)\r\n" );
document.write( "\r\n" );
document.write( "The denominator is the result of part (a) \r\n" );
document.write( "\r\n" );
document.write( "=  =  =  = about 0.595\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );