Answer:
the probability that there will be a seat available for every passenger who shows up is 0.74
Step-by-step explanation:
if the probability of choosing a passenger that will not show up is 5% , then the probability of choosing a passenger that will show up is 95%.
Denoting event X= x passengers will show up from the total of 52 that purchased the ticket
Then P(X) follows a binomial probability distribution, since each passenger is independent from others. Thus
P(X) = n!/((n-x)!*x!)*p^x*(1-p)^(n-x)
where
n= total number of passengers hat purchased the ticket= 52
p= probability of choosing a passenger that will show up
x = number of passengers that will show up
therefore the probability that the number does not exceed the limit of 50 passengers is:
P(X≤50)= ∑P(X=i) from i=0 to i=50 =F(50)
where F(x) is the cumulative binomial probability distribution, then from tables:
P(X≤50)= F(50) = 0.74
therefore the probability that there will be a seat available for every passenger who shows up is 0.74
