document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198546>Question 1198546</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a What is the probability that the painting and building of the scenery takes exactly<BR>\n" );
document.write( "13 days?<BR>\n" );
document.write( "b What is the probability that the three tasks together take exactly 19 days?<BR>\n" );
document.write( "A school is staging a musical and must have the scenery and programs ready for<BR>\n" );
document.write( "the opening night. The following probabilities are estimated for the duration of the<BR>\n" );
document.write( "activities<BR>\n" );
document.write( "Task 5 days 6 days 7 days<BR>\n" );
document.write( "Build scenery 0.1 0.45 0.45<BR>\n" );
document.write( "Paint scenery 0.3 0.4 0.3<BR>\n" );
document.write( "Print programs 0.5 0.3 0.2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848281 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848281\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **a) Probability that painting and building the scenery takes exactly 13 days**\r<BR>\n" );
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document.write( "* **Possible combinations:**<BR>\n" );
document.write( "    * Build: 5 days, Paint: 8 days <BR>\n" );
document.write( "    * Build: 6 days, Paint: 7 days <BR>\n" );
document.write( "    * Build: 7 days, Paint: 6 days\r<BR>\n" );
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document.write( "* **Calculate probabilities:**<BR>\n" );
document.write( "    * Build: 5 days, Paint: 8 days: 0.1 (Build) * 0 (Paint) = 0<BR>\n" );
document.write( "    * Build: 6 days, Paint: 7 days: 0.45 (Build) * 0.3 (Paint) = 0.135<BR>\n" );
document.write( "    * Build: 7 days, Paint: 6 days: 0.45 (Build) * 0.4 (Paint) = 0.18\r<BR>\n" );
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document.write( "* **Total probability:** 0 + 0.135 + 0.18 = 0.315\r<BR>\n" );
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document.write( "**Therefore, the probability that painting and building the scenery takes exactly 13 days is 0.315.**\r<BR>\n" );
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document.write( "**b) Probability that all three tasks together take exactly 19 days**\r<BR>\n" );
document.write( "\n" );
document.write( "* **Possible combinations:**<BR>\n" );
document.write( "    * Build: 5 days, Paint: 6 days, Print: 8 days<BR>\n" );
document.write( "    * Build: 5 days, Paint: 7 days, Print: 7 days<BR>\n" );
document.write( "    * Build: 6 days, Paint: 5 days, Print: 8 days<BR>\n" );
document.write( "    * Build: 6 days, Paint: 6 days, Print: 7 days<BR>\n" );
document.write( "    * Build: 6 days, Paint: 7 days, Print: 6 days <BR>\n" );
document.write( "    * Build: 7 days, Paint: 5 days, Print: 7 days<BR>\n" );
document.write( "    * Build: 7 days, Paint: 6 days, Print: 6 days\r<BR>\n" );
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document.write( "* **Calculate probabilities for each combination:**<BR>\n" );
document.write( "    * (0.1 * 0.4 * 0.2) + (0.1 * 0.3 * 0.2) + (0.45 * 0.3 * 0.2) + (0.45 * 0.4 * 0.2) + (0.45 * 0.3 * 0.3) + (0.45 * 0.3 * 0.2) + (0.45 * 0.4 * 0.3) = 0.231\r<BR>\n" );
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document.write( "**Therefore, the probability that all three tasks together take exactly 19 days is 0.231.**<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );