document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=971730>Question 971730</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ten light bulbs are chosen from a manufacturing lot and tested. If the probability of any bulb being defective is 0.1, find the probabilities of the following events: (a) exactly 2 of the bulbs are defective; (b) no more than 3 of the bulbs are defective; (c) at least 9 of the bulbs are not defective. <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 #594127 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=594127\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Binomial distribution:<BR>\n" );
document.write( "exactly 2 bulbs defective  is 10C2 (0.1)^2 (0.9)^8= 0.194.  <BR>\n" );
document.write( "There are 45 ways two bulbs can be defective, and that is 10C2\r<BR>\n" );
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document.write( "No more than 3 are defective.  <BR>\n" );
document.write( "P (0) are defective = 0.9^10=0.3486 <BR>\n" );
document.write( "P(1) is defective = 10 *0.9^9 *0.1 = 0.3874 (the highest, because it is expected value)<BR>\n" );
document.write( "P(2) are defective=0.194 from above<BR>\n" );
document.write( "P(3) are defective= 10C3*(.9)^7 * (.1)^3= 0.057<BR>\n" );
document.write( "This sum is 0.987<BR>\n" );
document.write( "We want NO MORE THAN this, so that is the complement.  It is 0.013.\r<BR>\n" );
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document.write( "At least 9 of the bulbs are not defective.  That is the probability of (1) being defective and (0) being defective, which we computed above.  That is 0.7360. </SPAN>\n" );
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