document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1087906>Question 1087906</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the probability of this trial: x = 3, n = 5, and p = 0.65, where x is successes in n trials.<BR>\n" );
document.write( "a. 34%<BR>\n" );
document.write( "b. 14%<BR>\n" );
document.write( "c. 25% </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #702197 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=702197\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\">Given Information:\r<BR>\n" );
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document.write( "n = 5 (sample size), p = 0.65 (probability of success), k = 3 (number of successes; I'm using k in place of x)\r<BR>\n" );
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document.write( "Use the combination formula with n = 5 and k = 3\r<BR>\n" );
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document.write( "n C k = (n!)/(k!*(n-k)!)<BR>\n" );
document.write( "5 C 3 = (5!)/(3!*(5-3)!)<BR>\n" );
document.write( "5 C 3 = (5!)/(3!*2!)<BR>\n" );
document.write( "5 C 3 = (5*4*3!)/(3!*2!)<BR>\n" );
document.write( "5 C 3 = (5*4)/(2!)<BR>\n" );
document.write( "5 C 3 = (5*4)/(2*1)<BR>\n" );
document.write( "5 C 3 = 20/2<BR>\n" );
document.write( "5 C 3 = 10\r<BR>\n" );
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document.write( "With that combination in mind, we can find the following binomial probability\r<BR>\n" );
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document.write( "P(X = k) = (n C k)*(p)^(k)*(1-p)^(n-k)<BR>\n" );
document.write( "P(X = 3) = (5 C 3)*(0.65)^(3)*(1-0.65)^(5-3)<BR>\n" );
document.write( "P(X = 3) = (5 C 3)*(0.65)^(3)*(0.35)^(2)<BR>\n" );
document.write( "P(X = 3) = (10)*(0.65)^(3)*(0.35)^2<BR>\n" );
document.write( "P(X = 3) = (10)*(0.274625)*(0.1225)<BR>\n" );
document.write( "P(X = 3) = 0.336415625<BR>\n" );
document.write( "P(X = 3) = 0.34 (round to the nearest hundredth)<BR>\n" );
document.write( "P(X = 3) = <font color=red size=4>34%</font> which is the final answer. You move the decimal point 2 spots to the right to go from 0.34 to 34%</font> </SPAN>\n" );
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