document.write( "Question 1164269: Kevin installed a certain brand of automatic garage door opener that utilizes a transmitter control with four independent switches, each one set on or off. The receiver (wired to the door) must be set with the same pattern as the transmitter.
\n" ); document.write( "If four neighbors with the same type of opener set their switches independently, what is the probability of at least one pair of neighbors using the same settings? \n" ); document.write( "

Algebra.Com's Answer #788576 by ikleyn(52909) $\"\"$ $\"About$

You can put this solution on YOUR website!
.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " Wording seems to be complicated, but the problem is, actually, quite simple.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "With 4 switches, each of which can be in any of the two possible positions,\r\n" );
document.write( "\r\n" );
document.write( "there are   = 16  different setting for the control.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, the probability for every one single of 4 neighbors to have the same setting in his (or her) control is  \r\n" );
document.write( "(their controls are of the same construction (!) ).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The probability that NO ONE of 4 neighbors has the same setting is  .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The probability under the question is the COMPLEMENT to it, i.e.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    P = 1 -  = 1 - 0.7225 = 0.2275.     ANSWER\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Very nice probability problem (!)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Hope that I correctly use the technical terms in my post . . . \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Please do not forget to post your \"THANKS\" for my teaching.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );