document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1178696>Question 1178696</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Assume that male and female births are equally likely and that the birth of any<BR>\n" );
document.write( "child does not affect the probability of the gender of any other children. Find the probability of at most five girls in ten births. </SPAN>\n" );
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document.write( "The number of girls in 10 births is either less than 5, or equal to 5, or more than 5:<br><BR>\n" );
document.write( "P(less than 5 girls)+P(5 girls)+P(more than 5 girls) = 1<br><BR>\n" );
document.write( "Because the probabilities for male or female are the same,<br><BR>\n" );
document.write( "P(less than 5 girls) = P(more than 5 girls)<br><BR>\n" );
document.write( "So<br><BR>\n" );
document.write( "2*P(less than 5 girls) = 1-P(5 girls)<BR>\n" );
document.write( "P(less than 5 girls) = (1-P(5 girls))/2<br><BR>\n" );
document.write( "P(5) = C(10,5)*(0.5)^10 = 0.246 (to 3 decimal places)<br><BR>\n" );
document.write( "P(less than 5 girls) = (1-0.246)/2 = 0.377<br><BR>\n" );
document.write( "P(at most 5 girls) = P(less than 5 girls)+P(5 girls) = 0.377+0.246 = 0.623<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );