document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=328423>Question 328423</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A missile can be accidentally launched if two relays A and B both have failed. the probabilities of A and B failing  known to be 0.01 and 0.03 respectively. It is also known that B is more likely to fail(probability 0.06) if A has failed.<BR>\n" );
document.write( "a)What is the probability of an accidental missile launch?<BR>\n" );
document.write( "b)What is the probability that A will fail if B has failed?<BR>\n" );
document.write( "c)Are the events \"A fails\" and \"B fails\" statistically independent? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #235250 by </B><A HREF=/tutors/aboutme.mpl?userid=galactus><B>galactus(183)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=galactus><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=galactus><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=235250\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Probability B fails given A fails, P(B|A), is given as .06\r<BR>\n" );
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document.write( "P(A)=.01\r<BR>\n" );
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document.write( "P(B)=.03\r<BR>\n" );
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document.write( "part a would be the probability A and B fail, P(A and B)\r<BR>\n" );
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document.write( "P(B|A)=P(A and B)/P(A)\r<BR>\n" );
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document.write( ".06=P(A and B)/.01\r<BR>\n" );
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document.write( "P(A and B)=.0006\r<BR>\n" );
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document.write( "part b, P(A|B)=P(A and B)/P(B)\r<BR>\n" );
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document.write( "We now have P(A and B)=.0006 from part a. Use this to answer part b.\r<BR>\n" );
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document.write( "P(A|B)=.0006/.03=.02\r<BR>\n" );
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document.write( "part c, the events are independent if the occurence of one does not affect the occurence of the other. That is, if P(B|A)=P(B) or P(A|B)=P(A) they are independent.\r<BR>\n" );
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document.write( "Are they the same?.  </SPAN>\n" );
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