document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201996>Question 1201996</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The probability that fewer than 2 prefer brand C is </SPAN>\n" );
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document.write( "Answer:  <font color=red size=4>0.08704</font><BR>\n" );
document.write( "This value is exact without any rounding done to it.\r<BR>\n" );
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document.write( "Explanation:\r<BR>\n" );
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document.write( "n = 5 = sample size<BR>\n" );
document.write( "p = 0.6 = probability of success<BR>\n" );
document.write( "x = number of people, in the sample, who prefer brand C cola<BR>\n" );
document.write( "x is chosen from the set {0,1,2,3,4,5}\r<BR>\n" );
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document.write( "This is a binomial distribution problem because:<ul><li>There are two outcomes. A person likes the cola or they don't.</li><li>Each trial is independent of any other. One person doesn't influence another's tastes.</li><li>The probability someone likes the cola is the same for each trial.</li></ul>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)*(0.6^x)(1-0.6)^(5-x)<BR>\n" );
document.write( "B(x) = (5 C x)*(0.6^x)(0.4)^(5-x)\r<BR>\n" );
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document.write( "The nCx notation refers to the nCr formula.<BR>\n" );
document.write( "It is known as the binomial coefficient.\r<BR>\n" );
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document.write( "Compute the probability of getting x = 0 people who like the cola.<BR>\n" );
document.write( "B(x) = (5 C x)*(0.6^x)(0.4)^(5-x)<BR>\n" );
document.write( "B(0) = (5 C 0)*(0.6^0)(0.4)^(5-0)<BR>\n" );
document.write( "B(0) = 1*(0.6^0)(0.4)^5<BR>\n" );
document.write( "B(0) = 0.01024<BR>\n" );
document.write( "This value is exact without any rounding done to it.\r<BR>\n" );
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document.write( "Do a similar set of steps for x = 1<BR>\n" );
document.write( "B(x) = (5 C x)*(0.6^x)(0.4)^(5-x)<BR>\n" );
document.write( "B(1) = (5 C 1)*(0.6^1)(0.4)^(5-1)<BR>\n" );
document.write( "B(1) = 5*(0.6^1)*(0.4)^4<BR>\n" );
document.write( "B(1) = 0.0768<BR>\n" );
document.write( "This value is exact without any rounding done to it.\r<BR>\n" );
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document.write( "The phrasing \"fewer than 2\" means we will add up the results of B(0) and B(1) to get the final answer.<BR>\n" );
document.write( "P(fewer than 2) = B(0) + B(1)<BR>\n" );
document.write( "P(fewer than 2) = 0.01024 + 0.0768<BR>\n" );
document.write( "P(fewer than 2) = <font color=red>0.08704</font><BR>\n" );
document.write( "There's an 8.704% chance of getting fewer than 2 people in the sample that like brand C cola.\r<BR>\n" );
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document.write( "Here are some other binomial distribution problems for more practice.<BR>\n" );
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document.write( "Further Reading<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://math.libretexts.org/Bookshelves/Applied_Mathematics/Applied_Finite_Mathematics_(Sekhon_and_Bloom)/09%3A_More_Probability/9.01%3A_Binomial_Probability\">https://math.libretexts.org/Bookshelves/Applied_Mathematics/Applied_Finite_Mathematics_(Sekhon_and_Bloom)/09%3A_More_Probability/9.01%3A_Binomial_Probability</a><BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.mathsisfun.com/data/binomial-distribution.html\">https://www.mathsisfun.com/data/binomial-distribution.html</a><BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://en.wikipedia.org/wiki/Binomial_coefficient\">https://en.wikipedia.org/wiki/Binomial_coefficient</a><BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://stattrek.com/online-calculator/binomial\">https://stattrek.com/online-calculator/binomial</a><BR>\n" );
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