document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1036346>Question 1036346</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a certain population, the probability that a woman has red hair is 1/4. If a woman has red hair, the probability of her having freckles is 3/4. If she does not have red hair, the probability of her having freckles is 1/16 .<BR>\n" );
document.write( "Find the following probabilities. Enter your final answers in percent notation rounded to the nearest tenth.<BR>\n" );
document.write( "1)If a woman is chosen at random from the population, what is the probability that she will have freckles? My instructors hint was:  women may have freckles regardless of the color of their hair.<BR>\n" );
document.write( "2) If a woman will have freckles, what is the probability that she has red hair? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #651008 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=651008\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  In a certain population, the probability that a woman has red hair is 1/4. <BR>\n" );
document.write( "If a woman has red hair, the probability of her having freckles is 3/4.<BR>\n" );
document.write( "P(red) = 1/4 <BR>\n" );
document.write( "P(f | red) = 3/4 = P(red AND f)/P(red) <BR>\n" );
document.write( "So, P(red AND f) = P(red)*(3/4) = (1/4)(3/4) = 3/16<BR>\n" );
document.write( "Comment:: Use this for your problem #2.<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "If she does not have red hair, the probability of her having freckles is 1/16 .<BR>\n" );
document.write( "P(f |not red) = 1/16<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "Find the following probabilities. Enter your final answers in percent notation rounded to the nearest tenth.<BR>\n" );
document.write( "1)If a woman is chosen at random from the population, what is the probability that she will have freckles? My instructors hint was: women may have freckles regardless of the color of their hair.<BR>\n" );
document.write( "P(f) = P(f |red) + P(f |not red) = (3/4) + 1/16 = 13/16<BR>\n" );
document.write( "--------------------------------------------------------------<BR>\n" );
document.write( "2) If a woman will have freckles, what is the probability that she has red hair?<BR>\n" );
document.write( "P(red | f) = P(red AND f)/P(f) = (3/16)/(13/16) = 3/13<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "--------------  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );