People with type O-negative blood are universal donors whose blood can safely be given to anyone. Only 7.2% of the population has O-negative blood. A mobile blood center is visited by 20 donors in the afternoon. Let X denote the number of universal donors among them.
What is the probability that X is at least 2?

Question

Quizplus · Accepted Answer

We can model the number of universal donors among 20 donors as a binomial distribution with n=20 and p=0.072 (the probability of an individual having O-negative blood). 
We want to find P(X>=2), which can be calculated using the complement rule: 
P(X>=2) = 1 - P(X<2) 
= 1 - P(X=0) - P(X=1)
= 1 - (0.928)^20 - 20(0.072)(0.928)^19 
(Note: We can also use the binomial probability formula to directly calculate P(X>=2), but this involves more calculations.)

Using a calculator or software, we can find P(X>=2) = 0.427. Therefore, the best choice is (C).

People with Type O-Negative Blood Are Universal Donors Whose Blood