document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1083738>Question 1083738</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The probability that a randomly selected elementary or secondary school teacher from a city is a female is 0.66, holds a second job is 0.46, and is a female and holds a second job is 0.22. Find the probability that an elementary or secondary school teacher selected at random from this city is a female or holds a second job. <BR>\n" );
document.write( "-I've tried just about every way and I only have one more submission left on my homework to get it right. The most recent I did was [.66 + .46 - (.119)= .84 ] that was incorrect. I know I'm using the right formula P(A or B) = P(A) + P(B) - P(A and B) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #697791 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=697791\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I would say that P(A and B) = 0.22 was given to you directly.<BR>\n" );
document.write( "That gives you P(A or B) = 0.66 + 0.46 - 0.22 = 0.90 .<BR>\n" );
document.write( "Adding 0.66+0.46 you get all female teachers l<BR>\n" );
document.write( "plus all teachers with a second job,<BR>\n" );
document.write( "but that would be counting twice all female teachers with a second job,<BR>\n" );
document.write( "so you have to subtract the 0.22 that is female and works 2 jobs,<BR>\n" );
document.write( " <BR>\n" );
document.write( "You do not need to rely on formulas if you can use common sense.<BR>\n" );
document.write( "You can imagine the situation, and if you were a newspaper reporter,<BR>\n" );
document.write( "you would be interviewing some of those teachers for the human side of the story.<BR>\n" );
document.write( "Say there are 100 teachers.<BR>\n" );
document.write( "Of those, 66 are women. (The other 34 must be men).<BR>\n" );
document.write( "There are 22 female teachers with a second paid job.<BR>\n" );
document.write( "(They must be early in their careers, so they are poorly paid,<BR>\n" );
document.write( "and they are not supported by anyone else, so they need the extra income).<BR>\n" );
document.write( "The other 66-22=44 women teachers do not have a second job.<BR>\n" );
document.write( "(Some are paid very well because of seniority and having extra education;<BR>\n" );
document.write( "some are married to successful lawyers and doctors).<BR>\n" );
document.write( "There are 46 teachers that have a second job.<BR>\n" );
document.write( "Those must include the 22 female teachers who have a second job,<BR>\n" );
document.write( "but the other 46-22=24 must be male.<BR>\n" );
document.write( "They are 24 of the 34 male teachers who have no wife bringing home money,<BR>\n" );
document.write( "and need that second job to make ends meet. It's a rough life.<BR>\n" );
document.write( "So, you have only 34-24=10 male teachers who do not have a second job.<BR>\n" );
document.write( "Those are the lucky ones.<BR>\n" );
document.write( "The other 100-10=90 teachers are women who work hard at home when not teaching,<BR>\n" );
document.write( "or have a second job, or both. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );