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

`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`

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=(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`