document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198349>Question 1198349</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 	Assume that, when a child is born, the probability it is a girl is ½ and that the sex of the child does not depend on the sex of an older sibling. Find the probability distribution for the number of girls in a family with 4 children<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #831991 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=831991\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "It appears that the tutor @ewatrrr might have misread the question.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The task is to find the probability distribution for the number of girls in this family. The teacher wants a probability table showing all the possible outcomes, and associated probabilities.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Convention is to use the binomial distribution. However, I'll take a different approach.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "X = number of girls<BR>\n" );
document.write( "X ranges from X = 0 to X = 4\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The calculation @ewatrrr has provided applies to both X = 0 girls (aka 4 boys) and also X = 4 girls (0 boys) due to symmetry.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "B = boy<BR>\n" );
document.write( "G = girl\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "X = 0 girls<BR>\n" );
document.write( "BBBB\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "X = 1 girl<BR>\n" );
document.write( "BBBG<BR>\n" );
document.write( "BBGB<BR>\n" );
document.write( "BGBB<BR>\n" );
document.write( "GBBB<BR>\n" );
document.write( "There are four cases where the family has 1 girl<BR>\n" );
document.write( "We can see this using the nCr formula with n = 4 and r = 1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "X = 2 girls<BR>\n" );
document.write( "BBGG<BR>\n" );
document.write( "BGGB<BR>\n" );
document.write( "BGBG<BR>\n" );
document.write( "GBBG<BR>\n" );
document.write( "GBGB<BR>\n" );
document.write( "GGBB<BR>\n" );
document.write( "There are six cases where the family has 2 girls<BR>\n" );
document.write( "This value (6) can be calculated by computing the nCr value when n = 4 and r = 2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "X = 3 girls<BR>\n" );
document.write( "GGGB<BR>\n" );
document.write( "GGBG<BR>\n" );
document.write( "GBGG<BR>\n" );
document.write( "BGGG<BR>\n" );
document.write( "There are four cases where the family has 3 girls (notice the similar structure to the X = 1 girl case)<BR>\n" );
document.write( "This value (4) can be calculated by computing the nCr value when n = 4 and r = 3.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "X = 4 girls<BR>\n" );
document.write( "GGGG<BR>\n" );
document.write( "There is one case where the family has 3 girls (notice the similar structure to the X = 0 girls case)<BR>\n" );
document.write( "There's no need to use nCr here, but if you wanted then it would be n = 4 and r = 4.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "There are 2^4 = 16 ways to have four kids.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This is the probability distribution<BR>\n" );
document.write( "<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >X</TD><TD >P(X)</TD></tr><tr><TD >0</TD><TD >1/16</TD></tr><tr><TD >1</TD><TD >4/16</TD></tr><tr><TD >2</TD><TD >6/16</TD></tr><tr><TD >3</TD><TD >4/16</TD></tr><tr><TD >4</TD><TD >1/16</TD></tr>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "Thing to notice: The numerators 1,4,6,4,1 are found in the same row of Pascal's Triangle<BR>\n" );
document.write( "I decided to not reduce the fractions to keep the denominators consistent.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This is what it looks like after reducing those fractions<BR>\n" );
document.write( "<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >X</TD><TD >P(X)</TD></tr><tr><TD >0</TD><TD >1/16</TD></tr><tr><TD >1</TD><TD >1/4</TD></tr><tr><TD >2</TD><TD >3/8</TD></tr><tr><TD >3</TD><TD >1/4</TD></tr><tr><TD >4</TD><TD >1/16</TD></tr>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "Another thing to notice: The P(X) values add to 1.<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );