document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1029575>Question 1029575</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that E and A are events in the sample space S. Suppose P(E|A)= 1/3 and P(E|A')=1/3. Is it necessarily true that P(E)=1/3? If yes, justify algebraically. If no, find sample space S and events A and E that satisfy P(E|A)= 1/3 and P(E|A')=1/3 and P(E) =/= 1/3. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #644545 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=644545\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Yes - <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large P(E) = P(E \mid A) \cdot P(A) + P(E \mid \overline{A}) \cdot P(\overline{A})\">. Using the given facts, this simplifies to <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large P(E) = \frac{1}{3} \cdot P(A) + \frac{1}{3} \cdot P(\overline{A}) = \frac{1}{3} \cdot (P(A) + P(\overline{A}) = \frac{1}{3}\">. </SPAN>\n" );
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