document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1132436>Question 1132436</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Here’s a question we were unsure of. \r<BR>\n" );
document.write( "\n" );
document.write( "According to a study of the numbers of male and female children in families in a certain population, a model has been determined that for any subsequent children, the probability that they will be of the same gender as the previous child is 3/5. Using this model, calculate the probability that, in a randomly chosen family of 3 children, there will be;<BR>\n" );
document.write( "a) 2 males and 1 female<BR>\n" );
document.write( "b) at least one female\r<BR>\n" );
document.write( "\n" );
document.write( "Hence, construct the probability distribution table of X if X is the number of female selected among the 3 children.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #749481 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=749481\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "We need to assume that there is equal probability that the first child is male or female.  After that, the probability is 3/5 that the next child will be the same gender and 2/5 that it will be different.  Then...<br><BR>\n" );
document.write( "(1) all male<br><BR>\n" );
document.write( "P(MMM) = (1/2)(3/5)(3/5) = 9/50<br><BR>\n" );
document.write( "(2) 2 male, 1 female<br><BR>\n" );
document.write( "P(MMF) = (1/2)(3/5)(2/5) = 6/50<BR>\n" );
document.write( "P(MFM) = (1/2)(2/5)(2/5) = 4/50<BR>\n" );
document.write( "P(FMM) = (1/2)(2/5)(3/5) = 6/50<BR>\n" );
document.write( "total 16/50<br><BR>\n" );
document.write( "(3) 1 male, 2 female<br><BR>\n" );
document.write( "P(MFF) = (1/2)(2/5)(3/5) = 6/50<BR>\n" );
document.write( "P(FMF) = (1/2)(2/5)(2/5) = 4/50<BR>\n" );
document.write( "P(FFM) = (1/2)(3/5)(2/5) = 6/50<BR>\n" );
document.write( "total 16/50<br><BR>\n" );
document.write( "(4) all female<br><BR>\n" );
document.write( "P(FFF) = (1/2)(3/5)(3/5) = 9/50<br><BR>\n" );
document.write( "Note that the sum of all the probabilities is 1, giving confidence that the calculations were correct.<br><BR>\n" );
document.write( "You can use the probabilities shown to answer the questions that were asked. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );