document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1172797>Question 1172797</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a lot there are 1100 pieces, 19% of them are broken. We choose randomly, successively, without adding them back, 3 pieces from the lot. What's the probability that:<BR>\n" );
document.write( "a) 2 out of 3 extracted pieces are broken?<BR>\n" );
document.write( "b) Maximum 1 piece is broken?<BR>\n" );
document.write( "c) The second piece to be broken?<BR>\n" );
document.write( "d) The third piece to be broken? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #797967 by </B><A HREF=/tutors/aboutme.mpl?userid=VFBundy><B>VFBundy(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=VFBundy><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=VFBundy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=797967\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If there are 1100 pieces in a lot, and 19% of them are broken, this means that exactly 209 pieces are broken (1100 * 0.19 = 209), while the remaining 891 pieces are not broken (1100 - 209 = 891).<BR>\n" );
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document.write( "<i>a) 2 out of 3 extracted pieces are broken?</i><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28209%2F1100%29+%2A+%28208%2F1099%29+%2A+%28891%2F1098%29+%2A+%283%21%2F%282%21%2A1%21%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=146718%2F1675975 ALIGN=MIDDLE  ALT=\"146718%2F1675975\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <b>0.0875</b><BR>\n" );
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document.write( "<i>b) Maximum 1 piece is broken?</i><BR>\n" );
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document.write( "We want to figure out the probability that exactly ONE piece is broken AND the probability that NONE of the pieces are broken.<BR>\n" );
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document.write( "Probability exactly ONE piece is broken:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28209%2F1100%29+%2A+%28891%2F1099%29+%2A+%28890%2F1098%29+%2A+%283%21%2F%281%21%2A2%21%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=502227%2F1340780 ALIGN=MIDDLE  ALT=\"502227%2F1340780\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.3746<BR>\n" );
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document.write( "Probability NONE of the pieces are broken:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28891%2F1100%29+%2A+%28890%2F1099%29+%2A+%28889%2F1098%29 ALIGN=MIDDLE  ALT=\"%28891%2F1100%29+%2A+%28890%2F1099%29+%2A+%28889%2F1098%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=101727%2F191540 ALIGN=MIDDLE  ALT=\"101727%2F191540\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.5311<BR>\n" );
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document.write( "Probability maximum one piece is broken:<BR>\n" );
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document.write( "0.3746 + 0.5311 = <b>0.9057</b><BR>\n" );
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document.write( "<i>c) The second piece to be broken?</i><BR>\n" );
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document.write( "Probability first piece is broken and second piece is broken:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28209%2F1100%29+%2A+%28208%2F1099%29 ALIGN=MIDDLE  ALT=\"%28209%2F1100%29+%2A+%28208%2F1099%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=988%2F27475 ALIGN=MIDDLE  ALT=\"988%2F27475\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.0360<BR>\n" );
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document.write( "Probability first piece is NOT broken and second piece is broken:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28891%2F1100%29+%2A+%28209%2F1099%29 ALIGN=MIDDLE  ALT=\"%28891%2F1100%29+%2A+%28209%2F1099%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16929%2F109900 ALIGN=MIDDLE  ALT=\"16929%2F109900\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.1540<BR>\n" );
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document.write( "Probability second piece is broken:<BR>\n" );
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document.write( "0.0360 + 0.1540 = <b>0.1900</b><BR>\n" );
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document.write( "<i>d) The third piece to be broken?</i><BR>\n" );
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document.write( "Probability first piece is broken, second piece is broken, and third piece is broken:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28209%2F1100%29+%2A+%28208%2F1099%29+%2A+%28207%2F1098%29 ALIGN=MIDDLE  ALT=\"%28209%2F1100%29+%2A+%28208%2F1099%29+%2A+%28207%2F1098%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11362%2F1675975 ALIGN=MIDDLE  ALT=\"11362%2F1675975\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.0068<BR>\n" );
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document.write( "Probability first piece is broken, second piece is NOT broken, and third piece is broken:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28209%2F1100%29+%2A+%28891%2F1099%29+%2A+%28208%2F1098%29 ALIGN=MIDDLE  ALT=\"%28209%2F1100%29+%2A+%28891%2F1099%29+%2A+%28208%2F1098%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48906%2F1675975 ALIGN=MIDDLE  ALT=\"48906%2F1675975\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.0292<BR>\n" );
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document.write( "Probability first piece is NOT broken, second piece is broken, and third piece is broken:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28891%2F1100%29+%2A+%28209%2F1099%29+%2A+%28208%2F1098%29 ALIGN=MIDDLE  ALT=\"%28891%2F1100%29+%2A+%28209%2F1099%29+%2A+%28208%2F1098%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48906%2F1675975 ALIGN=MIDDLE  ALT=\"48906%2F1675975\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.0292<BR>\n" );
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document.write( "Probability first piece is NOT broken, second piece is NOT broken, and third piece is broken:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28891%2F1100%29+%2A+%28890%2F1099%29+%2A+%28209%2F1098%29 ALIGN=MIDDLE  ALT=\"%28891%2F1100%29+%2A+%28890%2F1099%29+%2A+%28209%2F1098%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=167409%2F1340780 ALIGN=MIDDLE  ALT=\"167409%2F1340780\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.1249<BR>\n" );
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document.write( "Probability third piece is broken:<BR>\n" );
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document.write( "0.0068 + 0.0292 + 0.0292 + 0.1249 = <b>0.1901</b> </SPAN>\n" );
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