Answer:
[tex] P(X=0)[/tex]
And using the probability mass function we got:
[tex]P(X=0)=(4C0)(0.85)^0 (1-0.85)^{4-0}=0.000506[/tex]
Step-by-step explanation:
Let X the random variable of interest "number of children covered by some type of health insurance", on this case we now that:
[tex]X \sim Binom(n=4, p=0.85)[/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=0)[/tex]
And using the probability mass function we got:
[tex]P(X=0)=(4C0)(0.85)^0 (1-0.85)^{4-0}=0.000506[/tex]
