Answer:
[tex] P(X \geq 1) = 1- P(X<1) =1-P(X=0)[/tex]
We can use the probability mass function and we have this probability:
[tex]P(X=0)=(4C0)(0.54)^0 (1-0.54)^{4-0}=0.0448[/tex]
And replacing we got:
[tex] P(X \geq 1) =1- 0.0448 = 0.955[/tex]
Step-by-step explanation:
Let X the random variable of interest "number of people vaccinated", on this case we now that:
[tex]X \sim Binom(n=4, p=0.54)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
And we want to find this probability:
[tex] P(X \geq 1) = 1- P(X<1) =1-P(X=0)[/tex]
We can use the probability mass function and we have this probability:
[tex]P(X=0)=(4C0)(0.54)^0 (1-0.54)^{4-0}=0.0448[/tex]
And replacing we got:
[tex] P(X \geq 1) =1- 0.0448 = 0.955[/tex]
