Based on the u. s. census bureau’s american community survey of 2017, 12.9% of the u. s. population was foreign-born. the u. s. census bureau uses the term foreign-born to refer to anyone who is not a u. s. citizen at birth. when i took a sample of 5 students from my statistics class find the following probabilities:

1 find the probability that none of the students are foreign-born (x=0)
2 find p(x> =1) (that at least one is foreign-born)

1) 50.13% probability that none of the students are foreign-born (x=0)

2) 49.87% probability that at least one is foreign-born.

Step-by-step explanation:

For each student sampled, there are only two possible outcomes. Either they are foreign-born, or they are not. This means that we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinatios of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

In this problem we have that:

1 Find the probability that none of the students are foreign-born (x=0)

There is a 50.13% probability that none of the students are foreign-born (x=0)

2 find p(x>=1) (that at least one is foreign-born)

Either no students are foreign-born, or at least one is. The sum of the probabilities of these events is decimal 1.

There is a 49.87% probability that at least one is foreign-born.