document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=982727>Question 982727</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi. I need help with this binomial probability problem. <BR>\n" );
document.write( "Suppose that an unfair coin comes up heads 56.9% of the time. The coin is flipped a total of 27 times.<BR>\n" );
document.write( "1. What is the probability that you get at most 25 heads?\r<BR>\n" );
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document.write( "Given:<BR>\n" );
document.write( "An unfair die with heads 56.9% of the time.<BR>\n" );
document.write( "Find probability that up to 25 heads show up in 27 throws.<BR>\n" );
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document.write( "Solution:<BR>\n" );
document.write( "Binomial probability distribution,<BR>\n" );
document.write( "p=0.569<BR>\n" );
document.write( "n=27<BR>\n" );
document.write( "r=25<BR>\n" );
document.write( "So, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28n%2Cr%29=C%28n%2Cr%29%2Ap%5Er%2A%281-p%29%5E%28n-r%29 ALIGN=MIDDLE  ALT=\"P%28n%2Cr%29=C%28n%2Cr%29%2Ap%5Er%2A%281-p%29%5E%28n-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%2827%2C26%29=C%2827%2C26%29%2A0.569%5E26%2A%281-0.569%29%5E1=4.9976%2A10%5E-6 ALIGN=MIDDLE  ALT=\"P%2827%2C26%29=C%2827%2C26%29%2A0.569%5E26%2A%281-0.569%29%5E1=4.9976%2A10%5E-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%2827%2C27%29=C%2827%2C27%29%2A0.569%5E27%2A%281-0.569%29%5E0=2.444%2A10%5E-7 ALIGN=MIDDLE  ALT=\"P%2827%2C27%29=C%2827%2C27%29%2A0.569%5E27%2A%281-0.569%29%5E0=2.444%2A10%5E-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Therefore probability for getting up to 25 heads<BR>\n" );
document.write( "P(27,0-25)=1-P(27,>25)=1-P(27,26)-P(27,27)<BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-4.9976%2A10%5E%28-6%29-2.444%2A10%5E%28-7%29=1-5.242%2A10%5E%28-6%29=0.9999948 ALIGN=MIDDLE  ALT=\"1-4.9976%2A10%5E%28-6%29-2.444%2A10%5E%28-7%29=1-5.242%2A10%5E%28-6%29=0.9999948\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );