Respuesta :
Using the binomial distribution, it is found that there is a 0.9815 = 98.15% probability that at least one of them has been vaccinated.
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.
In this problem, the values of the parameters are:
n = 5, p = 0.55
The probability that at least one of them has been vaccinated is given by:
[tex]P(X \leq 1) = 1 - P(X = 0)[/tex]
In which:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.55)^{0}.(0,45)^{5} = 0.0185[/tex]
Then:
[tex]P(X \leq 1) = 1 - P(X = 0) = 1 - 0.0185 = 0.9815[/tex]
0.9815 = 98.15% probability that at least one of them has been vaccinated.
More can be learned about the binomial distribution at https://brainly.com/question/24863377
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