document.write( "Question 806542:
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #485898 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!
suppose three coins are lying on a table, two of them with heads facing up and one with tails facing up . one coin is chosen at random and flipped. what is the probability that after the flip the majority of coins ( i.e. at least two of them) will have _?_ facing up
\n" ); document.write( "

\r\n" );
document.write( "We start with 1H,2H,3T\r\n" );
document.write( "\r\n" );
document.write( "A.  We choose 1H to flip 1/3 of the time\r\n" );
document.write( "    1. 1H doesn't change and we end up with 1H,2H,3T \r\n" );
document.write( "       1/2 of 1/3 of the time or 1/6th of the time   \r\n" );
document.write( "    2. 1H changes and we end up with 1T,2H,3T \r\n" );
document.write( "       1/2 of 1/3 of the time or 1/6th of the time\r\n" );
document.write( "\r\n" );
document.write( "B.  We choose 2H to flip 1/3 of the time\r\n" );
document.write( "    1. 2H doesn't change and we end up with 1H,2H,3T \r\n" );
document.write( "       1/2 of 1/3 of the time or 1/6th of the time   \r\n" );
document.write( "    2. 2H changes and we end up with 1H,2T,3T \r\n" );
document.write( "       1/2 of 1/3 of the time or 1/6th of the time\r\n" );
document.write( "\r\n" );
document.write( "C.  We choose 3T to flip 1/3 of the time\r\n" );
document.write( "    1. 3T doesn't change and we end up with 1H,2H,3T \r\n" );
document.write( "       1/2 of 1/3 of the time or 1/6th of the time   \r\n" );
document.write( "    2. 3T changes and we end up with 1H,2H,3H \r\n" );
document.write( "       1/2 of 1/3 of the time or 1/6th of the time\r\n" );
document.write( "\r\n" );
document.write( "what is the probability that after the flip the majority of coins ( i.e. at\r\n" );
document.write( "least two of them) will have HEADS facing up.\r\n" );
document.write( "\r\n" );
document.write( "That will be P(A1 or B1 or C1 or C2) = 1/6 times 4 = 4/6 or 2/3. \r\n" );
document.write( "\r\n" );
document.write( "----\r\n" );
document.write( "\r\n" );
document.write( "what is the probability that after the flip the majority of coins ( i.e. at\r\n" );
document.write( "least two of them) will have TAILS facing up.\r\n" );
document.write( "\r\n" );
document.write( "That will be P(A2 or B2) = 1/6 times 2 = 2/6 or 1/3.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );