Question

In a large population, 54% of the people have been vaccinated. If 4 people are randomly selected, what is the probability that at least one of them has been vaccinated? Round your answer to three decimal places.

Answer 1

Answer:

$P(X \geq 1) = 1- P(X$

We can use the probability mass function and we have this probability:

$P(X=0)=(4C0)(0.54)^0 (1-0.54)^{4-0}=0.0448$

And replacing we got:

$P(X \geq 1) =1- 0.0448 = 0.955$

Step-by-step explanation:

Let X the random variable of interest "number of people vaccinated", on this case we now that:

$X \sim Binom(n=4, p=0.54)$

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:

$P(X \geq 1) = 1- P(X$

We can use the probability mass function and we have this probability:

$P(X=0)=(4C0)(0.54)^0 (1-0.54)^{4-0}=0.0448$

And replacing we got:

$P(X \geq 1) =1- 0.0448 = 0.955$