document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1087892>Question 1087892</A>: <I><SPAN STYLE=\"word-break: break-all;\"> you choose 3 batteries at random (with replacement) from a bag containing 10 batteries. Let x = the number of good batteries drawn. x/p(x)  0/.064 1/.288 2/.432 3/.216 What is the probability that at least one battery drawn is bad?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #702182 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=702182\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\"><BR>\n" );
document.write( "X = number of good batteries drawn\r<BR>\n" );
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document.write( "Lets define the following two events<BR>\n" );
document.write( "A = event that at least one battery is bad (1 battery is bad, 2 are bad, or all three are bad)<BR>\n" );
document.write( "B = event that 0 batteries are bad (all 3 batteries are good)\r<BR>\n" );
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document.write( "Note: another way to think of event A is to think of it as \"2 good batteries selected, 1 good battery selected, or 0 good batteries selected\".\r<BR>\n" );
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document.write( "According to the given table<BR>\n" );
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document.write( "We see that P(X = 3) = 0.216 which means P(B) = 0.216 is the probability of selecting all three batteries that are good\r<BR>\n" );
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document.write( "This means P(A) = 1-P(B) = 1-0.216 = <font color=red>0.784</font> is the final answer. It is the probability of selecting at least one bad battery (1 bad, 2 bad,or all 3 bad). \r<BR>\n" );
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document.write( "Note how A and B are complementary events. One event or the other, but not both, must happen. This is why P(A)+P(B) = 1.\r<BR>\n" );
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document.write( "Another way to get to the answer is to add up the probabilities for X = 0 on up to X = 2. This indicates we have as little as 0 good batteries on up to as much as 2 good batteries. So we have 0.064+0.288+0.432 = <font color=red>0.784</font> leading to the same answer.\r<BR>\n" );
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