Question

in a school district 85% of children are covered by some type of health insurance. If 4 children are selected at random, what is the probability that none are covered?

Answer 1

Answer:

$P(X=0)$

And using the probability mass function we got:

$P(X=0)=(4C0)(0.85)^0 (1-0.85)^{4-0}=0.000506$

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:

$X \sim Binom(n=4, p=0.85)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

And we want to find this probability:

$P(X=0)$

And using the probability mass function we got:

$P(X=0)=(4C0)(0.85)^0 (1-0.85)^{4-0}=0.000506$