document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1028147>Question 1028147</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If A and B are independent events, P(A) = 0.35, and P(B) = 0.25, find the probabilities below. (Enter your answers to four decimal places.)\r<BR>\n" );
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document.write( "(a)    P(A &#8745; B)<BR>\n" );
document.write( "(b)    P(A &#8746; B)<BR>\n" );
document.write( "(c)    P(A | B)<BR>\n" );
document.write( "(d)    P(Ac &#8746; Bc) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #643306 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=643306\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a) P(A &#8745; B) = P(A)P(B) = 0.35*0.25 = 0.0875, since A,B are independent.\r<BR>\n" );
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document.write( "(b) P(A &#8746; B) = P(A) + P(B) - P(A &#8745; B) = 0.35+0.25-0.0875 = 0.5125, by the addition law.\r<BR>\n" );
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document.write( "(c) P(A | B) = P(A &#8745; B)/P(B) = 0.0875/0.25 = 0.35\r<BR>\n" );
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document.write( "(d) P(Ac &#8746; Bc) = P(Ac) + P(Bc) - P(Ac &#8745; Bc) = P(Ac) + P(Bc) - P(Ac)P(Bc) = 1 - 0.35 + 1 - 0.25 - (1 - 0.35)(1 - 0.25) = 0.65 + 0.75 - 0.4875 = 0.9125, since if two events are independent then so are their complements. </SPAN>\n" );
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