document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190870>Question 1190870</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Distribution of blood types. All human blood can be “ABO-typed” as one of O, A, B, or AB, but the distribution of the types varies a bit among groups of people. Here is the distribution of blood types for a randomly chosen person in the United States:\r<BR>\n" );
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document.write( "Blood type     U.S. probability<BR>\n" );
document.write( "     A          0.42<BR>\n" );
document.write( "     B          0.11<BR>\n" );
document.write( "     AB         0.03<BR>\n" );
document.write( "     O          ?<BR>\n" );
document.write( "a)What is the probability of type O blood in the United States?<BR>\n" );
document.write( "b)Sasha has type A blood. She can safely receive blood transfusions from people with blood types O and A. What is the probability that a randomly chosen person from the United States can donate blood to Sasha? (This exercise and the one that follows ignore the Rh factor, another classification of blood types that is related to whether one person can donate blood to another.)<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #822613 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=822613\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Part (a)\r<BR>\n" );
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document.write( "Original Table<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >Blood type</TD><TD >U.S. probability</TD></tr><tr><TD >A</TD><TD >0.42</TD></tr><tr><TD >B</TD><TD >0.11</TD></tr><tr><TD >AB</TD><TD >0.03</TD></tr><tr><TD >O</TD><TD >?</TD></tr>\n" );
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document.write( "With any probability distribution, we need to have the following<ul><li>Every P(X) value is between 0 and 1, ie <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large 0 \le P(X) \le 1\"></li><li>All of the P(X) values add to 1 so that we account for 100% of every event possible.</li></ul>Let m be the missing probability in the table<BR>\n" );
document.write( "It must add with the other probabilities to get to 1.<BR>\n" );
document.write( "0.42+0.11+0.03+m = 1<BR>\n" );
document.write( "0.56+m = 1<BR>\n" );
document.write( "m = 1-0.56<BR>\n" );
document.write( "m = 0.44<BR>\n" );
document.write( "This tells us that 44% of patients in the US have type O blood.\r<BR>\n" );
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document.write( "This is what the table looks like with the missing item filled in properly<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >Blood type</TD><TD >U.S. probability</TD></tr><tr><TD >A</TD><TD >0.42</TD></tr><tr><TD >B</TD><TD >0.11</TD></tr><tr><TD >AB</TD><TD >0.03</TD></tr><tr><TD >O</TD><TD >0.44</TD></tr>\n" );
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document.write( "I'll let you check the two requirements I mentioned earlier.\r<BR>\n" );
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document.write( "Answer: 0.44\r<BR>\n" );
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document.write( "Part (b)\r<BR>\n" );
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document.write( "Add up the probabilities for type O and type A blood<BR>\n" );
document.write( "0.42+0.44 = 0.86\r<BR>\n" );
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document.write( "Answer: 0.86<BR>\n" );
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