document.write( "Question 1201670: Given events J and K: P(J) = .18; P(K) = .37; P(J OR K) = .45\r
\n" ); document.write( "\n" ); document.write( "Find P(J AND K).\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Find the probability of the complement of event (J AND K).\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Find the probability of the complement of event (J OR K). \n" ); document.write( "

Algebra.Com's Answer #836159 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Given events J and K: P(J) = .18; P(K) = .37; P(J OR K) = .45
\n" ); document.write( "Find P(J AND K).\r
\n" ); document.write( "\n" ); document.write( "Find the probability of the complement of event (J AND K).\r
\n" ); document.write( "\n" ); document.write( "Find the probability of the complement of event (J OR K).
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Start from this probability IDENTITY, which is valid for all/every/each events \r\n" );
document.write( "\r\n" );
document.write( "    P(J or K) = P(J) + P(K) - P(J and K).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Substitute here the given values.  You will get \r\n" );
document.write( "\r\n" );
document.write( "    0.45 = 0.18 + 0.37 - P(J and K).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From this equation, find  P(J and K)\r\n" );
document.write( "\r\n" );
document.write( "    P(J and K) = 0.18 + 0.37 - 0.45 = 0.1.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  P(J and K) = 0.1.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "To get the complementary probability, subtract the base probability from 1.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );