document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200654>Question 1200654</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 5. The prevalence of smoking among youth in a certain country is 18%. Suppose we select six individuals from the youth<BR>\n" );
document.write( "a. What is the probability that at least one is a smoker? <BR>\n" );
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document.write( "Answer: <font color=red>0.6960 (approximate)</font>\r<BR>\n" );
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document.write( "Work Shown:\r<BR>\n" );
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document.write( "n = 6 = sample size<BR>\n" );
document.write( "p = 0.18 = probability of picking a smoker<BR>\n" );
document.write( "x = number of smokers chosen, which is some value between 0 and 6.\r<BR>\n" );
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document.write( "Binomial Probability Distribution<BR>\n" );
document.write( "B(x) = (n C x)*(p^x)*(1-p)^(n-x)<BR>\n" );
document.write( "B(x) = (6 C x)*(0.18^x)*(1-0.18)^(6-x)<BR>\n" );
document.write( "B(0) = (6 C 0)*(0.18^0)*(1-0.18)^(6-0)<BR>\n" );
document.write( "B(0) = (1)*(0.18^0)*(1-0.18)^(6-0)<BR>\n" );
document.write( "B(0) = 0.304006671424<BR>\n" );
document.write( "The probability of selecting zero smokers is 0.304006671424\r<BR>\n" );
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document.write( "Subtract that from 1 to determine the probability of selecting at least one smoker.\r<BR>\n" );
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document.write( "Why does this work? Because,<BR>\n" );
document.write( "P(zero smokers)+P(at least one smoker) = 1<BR>\n" );
document.write( "P(at least one smoker) = 1-P(zero smokers)<BR>\n" );
document.write( "P(at least one smoker) = 1-0.304006671424<BR>\n" );
document.write( "P(at least one smoker) = 0.695993328576<BR>\n" );
document.write( "P(at least one smoker) = <font color=red>0.6960</font><BR>\n" );
document.write( "There's about a 69.60% chance of picking at least one smoker.\r<BR>\n" );
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document.write( "Further Reading<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://stats.libretexts.org/Courses/Highline_College/Book%3A_Statistics_Using_Technology_(Kozak)/05%3A_Discrete_Probability_Distributions/5.02%3A_Binomial_Probability_Distribution\">https://stats.libretexts.org/Courses/Highline_College/Book%3A_Statistics_Using_Technology_(Kozak)/05%3A_Discrete_Probability_Distributions/5.02%3A_Binomial_Probability_Distribution</a>\r<BR>\n" );
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document.write( "Useful online binomial calculators<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( "<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( "and here is a resource for TI84 calculators<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>\r<BR>\n" );
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document.write( "Similar problem<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1200582.html\">https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1200582.html</a><BR>\n" );
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