document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=938149>Question 938149</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a manufacturer knows that in a box of 120 light bulbs there will be 3 defective bulbs. Ben picks 2 bulbs from the box. determine the probability that he will pick a) 2 defective bulbs and b) exactly 1 defective bulb.\r<BR>\n" );
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document.write( ".. please help.. assigment is due tomorrow, test in 2 days and i cant figure out the answer to these kinda questions. i tried everything but i dont know where to even start with this type of question.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #571586 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=571586\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F120=1%2F40 ALIGN=MIDDLE  ALT=\"3%2F120=1%2F40\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the bulbs are defective,<BR>\n" );
document.write( "so the probability of Ben's first pick being defective is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F40 ALIGN=MIDDLE  ALT=\"1%2F40\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "and the probability of Ben's first pick being good is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-1%2F40=39%2F40 ALIGN=MIDDLE  ALT=\"1-1%2F40=39%2F40\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
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document.write( "a) If Ben's first pick is defective,<BR>\n" );
document.write( "he will have 119 light bulbs for his second choice,<BR>\n" );
document.write( "and 2 of those will be defective.<BR>\n" );
document.write( "So, the probability of picking a second defective bulb after picking the first defective bulb is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F119 ALIGN=MIDDLE  ALT=\"2%2F119\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "All in all, the probability that Ben will pick 2 defective bulbs is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F40%29%2A%282%2F119%29=1%2F%2820%2A119%29=1%2F2380 ALIGN=MIDDLE  ALT=\"%281%2F40%29%2A%282%2F119%29=1%2F%2820%2A119%29=1%2F2380\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That is about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.00042=%220.042%25%22 ALIGN=MIDDLE  ALT=\"0.00042=%220.042%25%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
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document.write( "On the other hand, if Ben's first pick is a good bulb,<BR>\n" );
document.write( "he will have 119 bulbs to choose from, 3 of them defective, along with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=119-3=116 ALIGN=MIDDLE  ALT=\"119-3=116\"   DISABLED_style= \"max-width:90%; height:auto;\" > good bulbs.<BR>\n" );
document.write( "So, the probability of Ben picking a second good bulb after picking the first good bulb is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=116%2F119 ALIGN=MIDDLE  ALT=\"116%2F119\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "All in all, the probability that Ben will pick 2 good bulbs is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2839%2F40%29%2A%28116%2F119%29=39%2A116%2F%2840%2A119%29=39%2A58%2F%2820%2A119%29=2262%2F2380=1131%2F1190 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
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document.write( "b) If Ben's chosen bulbs are neither both defective, nor both good bulbs, Ben will have picked exactly 1 defective bulb.<BR>\n" );
document.write( "The probability of that is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-1%2F2380-2262%2F2380=%282380-1-22622%29%2F2380=117%2F2380 ALIGN=MIDDLE  ALT=\"1-1%2F2380-2262%2F2380=%282380-1-22622%29%2F2380=117%2F2380\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That is about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.049=%224.9%25%22 ALIGN=MIDDLE  ALT=\"0.049=%224.9%25%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
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document.write( "Another way to get at the part b) answer is adding up<BR>\n" );
document.write( "the probability of first bulb defective, second bulb good, plus<BR>\n" );
document.write( "the probability of first bulb good, second bulb defective.<BR>\n" );
document.write( "That would be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F40%29%28117%2F119%29%2B%2839%2F40%29%283%2F119%29=117%2F%2840%2A119%29%2B39%2A3%2F%2840%2A119%29=117%2F%2840%2A119%29%2B117%2F%2840%2A119%29=117%2F%2820%2A119%29=117%2F2380 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "When two ways to solve the problem yield the same result, I am happy. </SPAN>\n" );
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