document.write( "Question 460322: consider the venn diagram below.
\n" ); document.write( "
\n" ); document.write( "Determine: n(A)
\n" ); document.write( " n(B)
\n" ); document.write( " p(A)
\n" ); document.write( " p(B)
\n" ); document.write( " p(A|B)
\n" ); document.write( " p(B|A)\r
\n" ); document.write( "\n" ); document.write( "Thanks very much for your help!
\n" ); document.write( " \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #315736 by Edwin McCravy(20086) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "

\r\n" );
document.write( "n(A) \r\n" );
document.write( "That's the number of elements in the whole red circle.\r\n" );
document.write( "There are 20 in the left part of the red circle and 50 \r\n" );
document.write( "in the right part. So that's 20+50 = 70. \r\n" );
document.write( "n(A) = 70 \r\n" );
document.write( "\r\n" );
document.write( "-----------------------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "n(B)\r\n" );
document.write( "That's the number of elements in the whole green circle.\r\n" );
document.write( "There are 50 in the left part of the green circle and 70 \r\n" );
document.write( "in the right part. So that's 50+70 = 120. \r\n" );
document.write( "n(B) = 120 \r\n" );
document.write( "\r\n" );
document.write( "-----------------------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "p(A)= n(A)/n(U)\r\n" );
document.write( "\r\n" );
document.write( "The universal set U consists of all the elements in both\r\n" );
document.write( "circles which is 20+50+70 or 140.\r\n" );
document.write( "\r\n" );
document.write( "So p(A) = n(A)/n(U) = 70/140 = 1/2\r\n" );
document.write( " \r\n" );
document.write( "p(B) = n(B)/n(U) = 120/140 = 6/7\r\n" );
document.write( "\r\n" );
document.write( "-----------------------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "p(A|B) = The probability of A given B.\r\n" );
document.write( "\r\n" );
document.write( "Since we are given that we are in B, we can cross out\r\n" );
document.write( "the 20 because those 20 are not in B, so we just have this:\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "So p(A|B) = 50/(50+70) = 50/120 = 5/12\r\n" );
document.write( "\r\n" );
document.write( "----------------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "p(B|A) \r\n" );
document.write( "\r\n" );
document.write( "Since we are given that we are in A, we can cross out\r\n" );
document.write( "the 70 because those 70 are not in A, so we just have this:\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "So p(B|A) = 50/(20+50) = 50/70 = 5/7\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( " \n" ); document.write( "

\n" );