Question 1168965
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p = probability of success
p = probability someone showing up (ie actually boarding their flight)
p = 0.73


n = sample size
n = 6


x = number of people who show up (out of n = 6 people)
x = 3


We'll use the binomial probability distribution formula below
B(x) = (n C x)*(p^x)*(1-p)^(n-x)
B(3) = (6 C 3)*(0.73^3)*(1-0.73)^(6-3)
B(3) = 20*(0.73^3)*(0.27^3)
B(3) = 20*(0.73^3)*(0.27^3)
B(3) = 20*0.389017*0.019683
B(3) = 20*0.007657021611
B(3) = 0.15314043222
B(3) = 0.153
In a sample of 6 people, there's roughly a 15.3% chance of exactly 3 showing up and actually boarding their flight.


Note: The notation 6 C 3 refers to the nCr combination notation. You'll use the formula {{{nCr = (n!)/(r!*(n-r)!)}}} or you can use Pascals Triangle. 



Final Answer: 0.153

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