document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1027105>Question 1027105</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a city school, 70% of students have blue eyes, 45% have dark hair, and 30% have blue eyes and dark hair. What is the probability (rounded to the nearest whole percent) that a randomly selected student has dark hair, given that the student has blue eyes? </SPAN>\n" );
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document.write( "Question:<BR>\n" );
document.write( "In a city school, 70% of students have blue eyes, 45% have dark hair, and 30% have blue eyes and dark hair. What is the probability (rounded to the nearest whole percent) that a randomly selected student has dark hair, given that the student has blue eyes?<BR>\n" );
document.write( " <BR>\n" );
document.write( "Solution:<BR>\n" );
document.write( "An efficient way to approach these problems is <BR>\n" );
document.write( "1. define events<BR>\n" );
document.write( "2. express all given information in terms of events<BR>\n" );
document.write( "3. using known relationships, determine the unknown.<BR>\n" );
document.write( " <BR>\n" );
document.write( "1. define events:<BR>\n" );
document.write( "B=student has blue eyes<BR>\n" );
document.write( "D=student has dark hair<BR>\n" );
document.write( " <BR>\n" );
document.write( "2. express given information in terms of events<BR>\n" );
document.write( "P(B)=0.70<BR>\n" );
document.write( "P(D)=0.45<BR>\n" );
document.write( "P(B&cap;D)=0.30<BR>\n" );
document.write( " <BR>\n" );
document.write( "3. using known relationships (write down what you know), find unknown.<BR>\n" );
document.write( "Assume random sampling.<BR>\n" );
document.write( "P(D|B)=Probability of a randomly selected student has dark hair given she has blue eyes<BR>\n" );
document.write( "=P(D&cap;B)/P(B)  [ by definition of conditional probability ]<BR>\n" );
document.write( "=0.30/0.70<BR>\n" );
document.write( "= 3/7<BR>\n" );
document.write( "= 42.8%<BR>\n" );
document.write( "Answer: The required probability is 42.8%<BR>\n" );
document.write( " <BR>\n" );
document.write( "I will leave it to you to round to the nearest whole percent, as specified in the question. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );