document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=913619>Question 913619</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A fair coin is tossed three times and the events A, B, and C are defined as follows:\r<BR>\n" );
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document.write( "A:{ At least one head is observed } <BR>\n" );
document.write( "B:{ At least two heads are observed } <BR>\n" );
document.write( "C:{ The number of heads observed is odd }\r<BR>\n" );
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document.write( "Find the following probabilities by summing the probabilities of the appropriate sample points:\r<BR>\n" );
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document.write( "(a)  P(Ac) =  <BR>\n" );
document.write( "(b)  P(A&#8745;B) =  <BR>\n" );
document.write( "(c)  P(A&#8746;B&#8746;C) =  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #554616 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=554616\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> List out the sample space\r<BR>\n" );
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document.write( "HHH<BR>\n" );
document.write( "HHT<BR>\n" );
document.write( "HTH<BR>\n" );
document.write( "HTT\r<BR>\n" );
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document.write( "THH<BR>\n" );
document.write( "THT<BR>\n" );
document.write( "TTH<BR>\n" );
document.write( "TTT\r<BR>\n" );
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document.write( "There are 8 possible outcomes. Notice how 2^3 = 8.\r<BR>\n" );
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document.write( "For parts (a), (b) and (c), I will use the sample space to calculate the probabilities.\r<BR>\n" );
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document.write( "(a)\r<BR>\n" );
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document.write( "P(A^c) = P(no heads) = 1/8\r<BR>\n" );
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document.write( "(b)\r<BR>\n" );
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document.write( "P(A&#8745;B) = P(at least one head AND at least 2 heads) = P(At least 2 heads)\r<BR>\n" );
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document.write( "P(A&#8745;B) = P(At least 2 heads)\r<BR>\n" );
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document.write( "P(A&#8745;B) = 4/8\r<BR>\n" );
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document.write( "P(A&#8745;B) = 1/2\r<BR>\n" );
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document.write( "(c)\r<BR>\n" );
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document.write( "P(A&#8746;B&#8746;C) = P(at least one head OR at least 2 heads OR # heads odd)\r<BR>\n" );
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document.write( "P(A&#8746;B&#8746;C) = P(at least one head OR # heads odd)\r<BR>\n" );
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document.write( "P(A&#8746;B&#8746;C) = 7/8\r<BR>\n" );
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document.write( "Let me know if you need more help or if you need me to explain a step in more detail.<BR>\n" );
document.write( "Feel free to email me at <a  rel=nofollow HREF=\"mailto:jim_thompson5910@hotmail.com?Subject=I%20Need%20Algebra%20Help\">jim_thompson5910@hotmail.com</a><BR>\n" );
document.write( "or you can visit my website here: <a  rel=nofollow HREF=\"http://www.freewebs.com/jimthompson5910/home.html\">http://www.freewebs.com/jimthompson5910/home.html</a>\r<BR>\n" );
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document.write( "Thanks,\r<BR>\n" );
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document.write( "Jim  </SPAN>\n" );
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