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Sagot :
Using the binomial distribution, there is a 0.0874 = 8.74% probability that not enough seats will be available.
What is the binomial distribution formula?
The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
For this problem, the values of the parameters are given by:
n = 15, p = 0.85.
The probability that not enough seats will be available is P(X = 15), as the only outcome in which not enough seats will be available is when all 15 people who bought the ticket show up, hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 15) = C_{15,15}.(0.85)^{15}.(0.15)^{0} = 0.0874[/tex]
0.0874 = 8.74% probability that not enough seats will be available.
More can be learned about the binomial distribution at https://brainly.com/question/24863377
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