document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1180971>Question 1180971</A>: <I><SPAN STYLE=\"word-break: break-all;\"> using the bionomial distribution find probabilities ??<BR>\n" );
document.write( "3 success in 8 trails when p=0.4 <BR>\n" );
document.write( "2 failure in 6 trails when p=0.6 <BR>\n" );
document.write( "2 of fewer success in 9 trails when p=0.4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #810790 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13334)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=810790\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The calculation for binomial probability is well defined; you simply need to do the calculations.  You can do that as easily as we can.<br><BR>\n" );
document.write( "I will outline the calculation required for the first problem and leave the actual work for the rest of the problem to you.<br><BR>\n" );
document.write( "(1) 3 successes in 8 trials with p=0.4....<br><BR>\n" );
document.write( "(a) You need to choose 3 of the 8 trials to be the successful ones: C(8,3)<BR>\n" );
document.write( "(b) The probability of each of the 3 successes is 0.4: (0.4)^3<BR>\n" );
document.write( "(c) The probability of each of the 5 failures is 1-0.4=0.6: (0.6)^5<br><BR>\n" );
document.write( "ANSWER: (C(8,3))*((0.4)^3)*((0.6)^5))<br><BR>\n" );
document.write( "Use a calculator....<br><BR>\n" );
document.write( "The same calculation with different numbers is required for the other two problems.<br><BR>\n" );
document.write( "(2) 2 failures in 6 trials with p=0.6....<br><BR>\n" );
document.write( "Two notes about this one.<BR>\n" );
document.write( "(a) 2 failures in 6 trials means 4 successes.<BR>\n" );
document.write( "(b) The p=0.6 must be assumed to be the probability of a success<br><BR>\n" );
document.write( "(3) 2 or fewer successes in 9 trials with p=0.4<br><BR>\n" );
document.write( "For this one you will need to do the calculation 3 times -- with 0, 1, or 2 successes -- and add the three probabilities.<br><BR>\n" );
document.write( " </SPAN>\n" );
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