document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196639>Question 1196639</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A relief organization must track their supply and demand for various blood types. They estimate that about 46​% of the population in a country has Type O​ blood, ​42% Type​ A, 9​% Type​ B, and the rest Type AB. \r<BR>\n" );
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document.write( "​a) If someone volunteers to give​ blood, what is the probability that this​ donor: i) Has Type AB​ blood? ii) Has Type A or Type B​ blood? iii) Is not Type​ O?<BR>\n" );
document.write( "​b) Among four potential​ donors, what is the probability​ that: i) All are Type​ O? ii) None have Type AB​ blood? iii) Not all are Type​ A? iv) At least one person is Type​ B? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848411 by </B><A HREF=/tutors/aboutme.mpl?userid=ElectricPavlov><B>ElectricPavlov(122)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ElectricPavlov><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=848411\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **a) Probabilities for a Single Donor**\r<BR>\n" );
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document.write( "* **i) Has Type AB blood:** <BR>\n" );
document.write( "    * Probability = 100% - (46% + 42% + 9%) = 3%\r<BR>\n" );
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document.write( "* **ii) Has Type A or Type B blood:** <BR>\n" );
document.write( "    * Probability = 42% + 9% = 51%\r<BR>\n" );
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document.write( "* **iii) Is not Type O blood:** <BR>\n" );
document.write( "    * Probability = 100% - 46% = 54%\r<BR>\n" );
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document.write( "**b) Probabilities for Four Donors**\r<BR>\n" );
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document.write( "* **i) All are Type O:**<BR>\n" );
document.write( "    * Probability = (0.46) * (0.46) * (0.46) * (0.46) = 0.46^4 ≈ 0.0457 (or 4.57%)\r<BR>\n" );
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document.write( "* **ii) None have Type AB blood:**<BR>\n" );
document.write( "    * Probability of not having Type AB = 100% - 3% = 97% <BR>\n" );
document.write( "    * Probability that none have Type AB = (0.97) * (0.97) * (0.97) * (0.97) = 0.97^4 ≈ 0.8853 (or 88.53%)\r<BR>\n" );
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document.write( "* **iii) Not all are Type A:**<BR>\n" );
document.write( "    * Probability that all are Type A = (0.42) * (0.42) * (0.42) * (0.42) = 0.42^4 ≈ 0.0311 (or 3.11%)<BR>\n" );
document.write( "    * Probability that not all are Type A = 100% - 3.11% = 96.89%\r<BR>\n" );
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document.write( "* **iv) At least one person is Type B:**<BR>\n" );
document.write( "    * Probability that none are Type B = (1 - 0.09)^4 = 0.6860<BR>\n" );
document.write( "    * Probability that at least one person is Type B = 100% - 68.60% = 31.40%\r<BR>\n" );
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document.write( "**Note:** These calculations assume that the blood types of the donors are independent of each other.<BR>\n" );
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