document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=909197>Question 909197</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The probability of rain on a given day in September is 0.25.<BR>\n" );
document.write( "a) Assuming independent trials, what is the probability that there will be no rain over the three days of the Labour Day Weekend?<BR>\n" );
document.write( "b) Assuming independent trials, what is the probability that it will ran at least once in a given week?<BR>\n" );
document.write( "c) Assuming independent trials, what is the probability that it will rain twice in one week?<BR>\n" );
document.write( "d) What is the mean (i.e, expected) number of rainy days in September?<BR>\n" );
document.write( "e) Is the assumption of independent trials in this example realistic?\r<BR>\n" );
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document.write( "I am still new at these concepts and am having trouble solving. Any help would be greatly appreciated.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #551672 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=551672\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let X~Binomial(n=3,p=.25)\r<BR>\n" );
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document.write( "a) P[X=0] =  (3 choose 0)(.25)^0*(.75)^3 = .4219\r<BR>\n" );
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document.write( "Let X~Binomial(n=7, p=.25)\r<BR>\n" );
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document.write( "b) P[x>=1] = 1-P[X=0] = 1-(.75)^7 = .8665\r<BR>\n" );
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document.write( "c) P[X=2] = (7 choose 2)*(.25)^2*(.75)^5 = .3115\r<BR>\n" );
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document.write( "Let X~Binomial(n=30, p =.25)  [30 days in Sept]\r<BR>\n" );
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document.write( "d) Mean of a binomial = n*p.\r<BR>\n" );
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document.write( "30 * .25 = 7.5\r<BR>\n" );
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document.write( "e) I would say that assumption of independent trials is realistic. Just cause it rains today doesn't significantly change the probability of it raining the next day as well.<BR>\n" );
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