document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201524>Question 1201524</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Kind of a big one: \r<BR>\n" );
document.write( "\n" );
document.write( "Human blood is classified by the presence or absence of three main antigens (A, B, and Rh). When a blood specimen is typed, the presence of the A and/or B antigen is indicated by listing the letter A and/or the letter B. If neither the A nor the B antigen is present, the letter O is used.\r<BR>\n" );
document.write( "\n" );
document.write( "The following table gives the percent of a certain country's population having each of the eight possible blood types in the sample space. Note that the presence or absence of the Rh antigen is indicated by the symbols + or −, respectively.<BR>\n" );
document.write( "Blood Types percentage:	 A+ is 35.7	A− is 6.3	B+ is 9.5	B− is 1.5	AB+ is 3.4	AB− is 0.8	O+ is 37.2	O− is 5.6\r<BR>\n" );
document.write( "\n" );
document.write( "(a) What is the probability that a person selected randomly from the population has a blood type that is type O or Rh+?\r<BR>\n" );
document.write( "\n" );
document.write( "(b) What is the probability that a person selected randomly from the population has a blood type that contains the A antigen?\r<BR>\n" );
document.write( "\n" );
document.write( "(c) What is the probability that a person selected randomly from the population has a blood type that is type AB or Rh−? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #835937 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52803)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=835937\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Human blood is classified by the presence or absence of three main antigens (A, B, and Rh). <BR>\n" );
document.write( "When a blood specimen is typed, the presence of the A and/or B antigen is indicated <BR>\n" );
document.write( "by listing the letter A and/or the letter B. <BR>\n" );
document.write( "If neither the A nor the B antigen is present, the letter O is used.<BR>\n" );
document.write( "The following table gives the percent of a certain country's population <BR>\n" );
document.write( "having each of the eight possible blood types in the sample space. <BR>\n" );
document.write( "Note that the presence or absence of the Rh antigen is indicated <BR>\n" );
document.write( "by the symbols + or −, respectively.<BR>\n" );
document.write( "Blood Types percentage: <BR>\n" );
document.write( "A+ is 35.7 A− is 6.3 B+ is 9.5 B− is 1.5 AB+ is 3.4 AB− is 0.8 O+ is 37.2 O− is 5.6<BR>\n" );
document.write( "(a) What is the probability that a person selected randomly from the population <BR>\n" );
document.write( "    has a blood type that is type O or Rh+?<BR>\n" );
document.write( "(b) What is the probability that a person selected randomly from the population <BR>\n" );
document.write( "    has a blood type that contains the A antigen?<BR>\n" );
document.write( "(c) What is the probability that a person selected randomly from the population <BR>\n" );
document.write( "    has a blood type that is type AB or Rh−?<BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~~~~~~\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "Probably, persons with medical education read this table easily,\r\n" );
document.write( "but for me it is better to rewrite and to present it in other form.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "I will present this table horizontally with four upper lines of names\r\n" );
document.write( "\r\n" );
document.write( "Line 1       1    |    2    |   3    |   4    |   5    |    6    |    7    |   8\r\n" );
document.write( "Line 2       A+   |    A-   |   B+   |   B-   |   AB+  |    AB-  |    O+   |   O-\r\n" );
document.write( "\r\n" );
document.write( "Line 3       ABR  |    ABR  |   ABR  |   ABR  |   ABR  |    ABR  |    ABR  |   ABR\r\n" );
document.write( "Line 4       A R       A         BR       B       ABR       AB          R         \r\n" );
document.write( "\r\n" );
document.write( "Line 5       35.7      6.3      9.5      1.5      3.4       0.8       37.2     5.6\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Line 1 simply numerates the columns of the table.\r\n" );
document.write( "Line 2 is the standard medical designations of states.\r\n" );
document.write( "Line 3 contains the format ABR, repeated 8 times in 8 columns\r\n" );
document.write( "Line 4 shows the factual content (presence/absence)  of three main antigens \r\n" );
document.write( "                                 (A, B, or Rh; for the last, I use R for simplicity)\r\n" );
document.write( "Line 5 represents the given numbers.  \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "I checked that the sum of numbers in Line 5 is 100, representing 100%.\r\n" );
document.write( "It convinces me that the given info represents the disjoint states, that covers 100% space events.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(a)  What is the probability that a person selected randomly from the population \r\n" );
document.write( "     has a blood type that is type O or Rh+?\r\n" );
document.write( "\r\n" );
document.write( "     To answer (a), add the numbers  L(7), L(8), L(1), L(3), L(5)  from Line 5.\r\n" );
document.write( "                                     37.2 + 5.6+ 35.7+ 9.5 + 3.4 = 91.4.    <U>ANSWER</U> \r\n" );
document.write( "     Since you see from Line 2 or Line 4 that L(7) and L(8) are of type O; L(1), L(3), L(5) are of type Rh+.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(b)  What is the probability that a person selected randomly from the population \r\n" );
document.write( "     has a blood type that contains the A antigen?\r\n" );
document.write( " \r\n" );
document.write( "     To answer (b), add the numbers  L(1), L(2), L(5), L(6)  from Line 5.\r\n" );
document.write( "                                     35.7+ 6.3 + 3.4 + 0.8 = 46.2.          <U>ANSWER</U>\r\n" );
document.write( "     Since you see from Line 2 or Line 4 the presence of symbol \"A\" at these columns.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(c)  What is the probability that a person selected randomly from the population \r\n" );
document.write( "     has a blood type that is type AB or Rh−?\r\n" );
document.write( "\r\n" );
document.write( "     To answer (c), add L(5), L(6), L(4), L(6), L(8)  from Line 5.\r\n" );
document.write( "                        (If you just got the idea, perform this calc on your own).\r\n" );
document.write( "     Since you see from Line 2 or Line 4 the presence of symbols \"AB\" or \"-\" at these columns.\r\n" );
document.write( "</PRE>\r<BR>\n" );
document.write( "\n" );
document.write( "Solved.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Evaluating this problem &nbsp;\" in whole \" &nbsp;according to its complexity level, <BR>\n" );
document.write( "I'd say that it is quite stupid mechanical job.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "To be honest, &nbsp;I do not understand why the tutors should do &nbsp;(or are expected to do) &nbsp;so primitive assignments.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In any case, &nbsp;I hope you do understand everything in this solution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "*************************************\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "After completing this task, &nbsp;I think what useful you can learn from it.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I think, &nbsp;THIS &nbsp;LESSON &nbsp;would be useful for you:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "     In every part, they ask you about the probability of the union of some disjoint events.\r\n" );
document.write( "\r\n" );
document.write( "     Such probability is always the sum of probabilities of participating events.\r\n" );
document.write( "\r\n" );
document.write( "     The key word here is \"disjoint events\".\r\n" );
document.write( "</PRE>\r<BR>\n" );
document.write( "\n" );
document.write( "Good to memorize.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );