Answer:
[tex]P(x<4) =0.0473[/tex]
Step-by-step explanation:
Let's call p the probability that a passenger shows up.
Then we know that:
[tex]p = 0.85[/tex]
Then we took a sample of n = 6 passengers.
We can calculate the probability that less than 4 are presented using the binomial formula:
[tex]P(x) = \frac{n!}{x!(n-x)!}*p^x*(1-p)^{n-x}[/tex]
Where x is the number of passengers that show up, n is the number of selected passengers, p is the probability that a passenger shows up.
Then we look for:
[tex]P(x<4) = P(0) +P(1) +P(2) +P(3)=1-P(6)-P(5)-P(4)[/tex]
[tex]P(6) = \frac{6!}{6!(6-6)!}*0.85^6*(1-0.85)^{6-6}=0.37715[/tex]
[tex]P(5) = \frac{6!}{5!(6-5)!}*0.85^5*(1-0.85)^{6-5}=0.39933[/tex]
[tex]P(4) = \frac{6!}{4!(6-4)!}*0.85^4*(1-0.85)^{6-4}=0.17618[/tex]
[tex]P(x<4) =1-0.377-0.399-0.176[/tex]
[tex]P(x<4) =0.0473[/tex]
