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Answer:
There is a 27.62% probability that exactly 2 of the U.S. residents have blood type AB.
Step-by-step explanation:
For each U.S. resident, there are only two outcomes possible. Either they have blood type AB, or they do not. This means that we can solve this problem using binomial probability distribution concepts.
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 is the probability of X happening.
In this problem, we have that:
50 U.S residents are sampled, so
4% of the U.S population has blood type AB, so .
What is the probability that exactly 2 of the U.S. residents have blood type AB?
This is P(X = 2). So:
There is a 27.62% probability that exactly 2 of the U.S. residents have blood type AB.