document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=192160>Question 192160</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am not grasping probability at all!  I'm 36 years old and I have just returned back to school.  Can you please help?\r<BR>\n" );
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document.write( "A certain airplane has two independent alternatiors to provide electrical power.  The probability that a given alternator will fail on a 1-hour flight is .02.\r<BR>\n" );
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document.write( "What is the probability that (a) both fail? (b) neither will fail? (c) One or the other will fail? Show all steps carefully. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #144212 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=144212\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) The probability of both engines failing is simply the product of the individual probabilities. So...\r<BR>\n" );
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document.write( "p(both failing) = p(one failing)*p(other failing) <BR>\n" );
document.write( "p(both failing) = 0.2*0.2<BR>\n" );
document.write( "p(both failing) = 0.04\r<BR>\n" );
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document.write( "So the probability of both failing is 0.04 which is 1/25 or 4%\r<BR>\n" );
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document.write( "b) The probability of neither failing is the same as the probability of both NOT failing. So in this part, we're multiplying the probabilities of both engines NOT failing to get:\r<BR>\n" );
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document.write( "P(neither failing) = p(one NOT failing)*p(other NOT failing) <BR>\n" );
document.write( "P(neither failing) = (1-0.2)*(1-0.2) <BR>\n" );
document.write( "P(neither failing) = 0.8*0.8 <BR>\n" );
document.write( "P(neither failing) = 0.64\r<BR>\n" );
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document.write( "So the probability of neither failing is 0.64 which is 16/25 or 64% \r<BR>\n" );
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document.write( "Note: if x is the probability of an event occurring, then 1-x is the probability of the event NOT occurring.\r<BR>\n" );
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document.write( "c) To find the chances if one event or the other occurs, simply add the two individual probabilities and subtract out the probability that they will both occur (to remove duplicates):\r<BR>\n" );
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document.write( "P(one or other failing) = p(one failing) + p(other failing) - p(both failing)<BR>\n" );
document.write( "P(one or other failing) = 0.2 + 0.2 - 0.04 <BR>\n" );
document.write( "P(one or other failing) = 0.36\r<BR>\n" );
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document.write( "So the probability of either one failing (but not both) is 0.36 which is 9/25 or 36% \r<BR>\n" );
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