Question 1200654
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Answer: <font color=red>0.6960 (approximate)</font>


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Work Shown:


n = 6 = sample size
p = 0.18 = probability of picking a smoker
x = number of smokers chosen, which is some value between 0 and 6.


Binomial Probability Distribution
B(x) = (n C x)*(p^x)*(1-p)^(n-x)
B(x) = (6 C x)*(0.18^x)*(1-0.18)^(6-x)
B(0) = (6 C 0)*(0.18^0)*(1-0.18)^(6-0)
B(0) = (1)*(0.18^0)*(1-0.18)^(6-0)
B(0) = 0.304006671424
The probability of selecting zero smokers is 0.304006671424


Subtract that from 1 to determine the probability of selecting at least one smoker.

 
Why does this work? Because,
P(zero smokers)+P(at least one smoker) = 1
P(at least one smoker) = 1-P(zero smokers)
P(at least one smoker) = 1-0.304006671424
P(at least one smoker) = 0.695993328576
P(at least one smoker) = <font color=red>0.6960</font>
There's about a 69.60% chance of picking at least one smoker.


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Further Reading
<a 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>


Useful online binomial calculators
<a href = "https://www.omnicalculator.com/statistics/binomial-distribution">https://www.omnicalculator.com/statistics/binomial-distribution</a>
<a href = "https://www.gigacalculator.com/calculators/binomial-probability-calculator.php">https://www.gigacalculator.com/calculators/binomial-probability-calculator.php</a>
and here is a resource for TI84 calculators
<a href = "https://www.statology.org/binomial-probabilities-ti-84-calculator/">https://www.statology.org/binomial-probabilities-ti-84-calculator/</a>


Similar problem
<a 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>
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