document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201405>Question 1201405</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If 10% of the people who take a certain medication get a headache, find the probability that if 5 people take the medication, one will get a headache.\r<BR>\n" );
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document.write( "If 25% of U.S. prison inmates are not U.S. citizens, what is the probability of randomly selecting three inmates who will not be U.S. citizens?\r<BR>\n" );
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document.write( "If 30% of commuters ride to work on a bus, find the probability that if 8 workers are selected at random, 3 will ride the bus. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #835750 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=835750\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "The rules of this website is to post one question at a time. <BR>\n" );
document.write( "I'll do problem 1 to get you started.\r<BR>\n" );
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document.write( "We have a binomial process because:<BR>\n" );
document.write( "<ul><li>A person gets a headache or they don't. There are two outcomes.</li><li>Each person is independent of any other (eg: someone getting a headache won't cause another person to get a headache)</li><li>The probability of a headache is the same for any person (10%).</li></ul>n = 5 = sample size<BR>\n" );
document.write( "p = 0.10 = probability of a headache<BR>\n" );
document.write( "x = number of people, in the sample, that get a headache<BR>\n" );
document.write( "x is an integer in the set {0, 1, 2, 3, 4, 5}<BR>\n" );
document.write( "i.e. x is between 0 and 5 inclusive of both endpoints.\r<BR>\n" );
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document.write( "B(x) = binomial probability<BR>\n" );
document.write( "B(x) = (n C x)*(p^x)*(1-p)^(n-x)<BR>\n" );
document.write( "B(x) = (5 C x)*(0.10^x)*(1-0.10)^(5-x)<BR>\n" );
document.write( "B(x) = (5 C x)*(0.10^x)*(0.90)^(5-x)<BR>\n" );
document.write( "The nCx refers to the nCr combination formula.\r<BR>\n" );
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document.write( "Plug in x = 1 to determine the probability there's exactly one person with a headache in the sample of five people.<BR>\n" );
document.write( "B(x) = (5 C x)*(0.10^x)*(0.90)^(5-x)<BR>\n" );
document.write( "B(1) = (5 C 1)*(0.10^1)*(0.90)^(5-1)<BR>\n" );
document.write( "B(1) = (5)*(0.10^1)*(0.90)^4<BR>\n" );
document.write( "B(1) = <font color=red>0.32805</font>\r<BR>\n" );
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document.write( "The probability that there's exactly one headache is exactly <font color=red>0.32805</font><BR>\n" );
document.write( "This is exactly a 32.805% chance.\r<BR>\n" );
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document.write( "Here are a few binomial distribution calculators.<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.gigacalculator.com/calculators/binomial-probability-calculator.php\">https://www.gigacalculator.com/calculators/binomial-probability-calculator.php</a><BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.omnicalculator.com/statistics/binomial-distribution\">https://www.omnicalculator.com/statistics/binomial-distribution</a><BR>\n" );
document.write( "You could also use a spreadsheet or a TI83/TI84 calculator.\r<BR>\n" );
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document.write( "Here is an article talking about binomial probabilities using a TI84<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.statology.org/binomial-probabilities-ti-84-calculator/\">https://www.statology.org/binomial-probabilities-ti-84-calculator/</a><BR>\n" );
document.write( "Use the PDF rather than CDF because the goal is to calculate one single value (rather than add up a bunch of values).\r<BR>\n" );
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document.write( "Another question involving the binomial probability distribution<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1201351.html\">https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1201351.html</a>\r<BR>\n" );
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document.write( "Answer: <font color=red>0.32805</font><BR>\n" );
document.write( "This value is exact and hasn't been rounded.<BR>\n" );
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