document.write( "Question 1162428: P(E)=0.35, P(F)=0.35, P(E ∩ F)=0.15 and P((E ∪ F)c)=0.45. Find P(E ∩ FC|F)
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #786225 by ikleyn(52802) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "OK.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now i got everything in your post and in your designations (which you failed to disclose in the post).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(1)  The symbol \"c\" means \"the complement\" in each appearance.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(2)  The equality  P((E ∪ F)c)=0.45  is excessive and unnecessary,\r\n" );
document.write( "\r\n" );
document.write( "         since it follows from the preceding data:\r\n" );
document.write( "\r\n" );
document.write( "              P(E)=0.35, P(F)=0.35, P(E ∩ F)=0.15 implies  P(E U F) = P(E) + P(F) - P(E ∩ F) = 0.35 + 0.35 - 0.15 = 0.55,\r\n" );
document.write( "\r\n" );
document.write( "              which is exactly the same as  P((E ∪ F)c)=0.45.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(3)  Finally,  P(E ∩ FC|F) = by the definition  = P( (E ∩ FC) ∩ F) / P(F) = 0,\r\n" );
document.write( "\r\n" );
document.write( "       since the set  (E ∩ FC) ∩ F  is empty.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.   P(E ∩ FC|F) = 0.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved, deciphered, answered and completed.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The reader may consider it as a joke problem . . . \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The only thing that remained unclear to me is if the author of this post did understand that it was a joke problem . . . \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );