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Universal Blood Donors. People with type O-negative blood are referred to as universal donors, although if you give type O-negative blood to any patient, you run the risk of a transfusion reaction due to certain antibodies present in the blood. However, any patient can receive a transfusion of O-negative red blood cells. Only 7.2\% of the American population have O-negative blood. If 10 people appear at random to give blood, what is the probability that at least one of them is a universal donor?

Short Answer

Expert verified
The probability that at least one is a universal donor is about 50.86%.

Step by step solution

01

Understand the Problem

We want to find the probability that at least one of 10 randomly chosen people is a universal donor. This can be expressed as 1 minus the probability that none of them are universal donors.
02

Define the Event

Let's define the probability that a randomly selected person is NOT a universal donor. We know that 7.2% of the population have O-negative blood, so the probability that a person does NOT have O-negative blood is 1 - 0.072 = 0.928.
03

Calculate Probabilities for None

Next, we find the probability that none of the 10 people are universal donors, which means all of them have a blood type other than O-negative: \[ P(\text{none are universal donors}) = 0.928^{10} \]
04

Compute Probability of At Least One

Finally, the probability that at least one person is a universal donor is 1 minus the probability that none are:\[ P(\text{at least one is a universal donor}) = 1 - 0.928^{10} \]
05

Solve the Equation

Calculate the value:\[ 0.928^{10} \approx 0.4914 \]Then find:\[ 1 - 0.4914 = 0.5086 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Universal Donor
A universal donor is someone whose blood can be donated to individuals with any blood type without causing serious allergic or adverse reactions. Ultimately, this designation reduces complications during blood transfusions. People with O-negative blood are considered universal donors because their blood lacks the A and B antigens typically found on the surface of red blood cells. This absence of antigens means there is less risk for harmful immune reactions when their blood is introduced into the recipient's body.

Universal donors are highly valuable in emergency situations where blood type matching is not feasible. In these instances, O-negative blood can be used, potentially saving lives when time is critical.

Although the term "universal donor" highlights the flexibility and utility of O-negative blood, it is important to note that there are still rare occasions where a transfusion reaction can occur because of other antibodies present.
O-negative Blood
O-negative blood is unique in its chemical composition and characteristics. It is known as a universal donor type because it lacks the A and B antigens and does not have the Rh factor, which limits how it interacts with other blood types. These features make it highly adaptable, serving as a life-saving option for patients with different blood types.

Despite comprising only about 7.2% of the American population, individuals with O-negative blood are crucial to the blood donation system. Their contributions ensure hospitals and emergency rooms can respond efficiently to urgent transfusion needs without waiting for compatible matches. Blood banks encourage donations from individuals with this rare blood type to maintain a supply that meets unexpected demands.
Transfusion Reaction
Transfusion reactions occur when a recipient's immune system identifies donated blood as foreign and launches an immune response, potentially causing symptoms ranging from mild rashes to serious complications such as hemolysis. Though people with O-negative blood are considered universal donors, some recipients might still react to minor antigens or antibodies present in the donor blood.

The potential for transfusion reactions underscores the importance of careful screening and matching blood types wherever possible. Health professionals aim to minimize these occurrences by performing compatibility tests before transfusions. Despite all precautions, reactions can sometimes still occur, emphasizing the critical need for universal donor blood types to assist in emergency situations where time does not allow for such testing.
Random Selection
Random selection in the context of blood donation involves choosing individuals without any specific criteria to donate blood. This concept applies to statistical probability, often used in public health studies to predict the likelihood of certain events, such as the probability of finding a universal donor among a group.

In the exercise, when 10 people are chosen at random, the probability of at least one being a universal donor (O-negative) is calculated by considering the chance that none are universal donors. This is done using complementary probability – focusing on the opposite event and then subtracting from 1 to find the desired probability.

Random selection is pivotal in decision-making processes and helps researchers develop understanding through measurable statistical methods. It helps extrapolate data that inform public health policies and operational strategies in blood donation services.

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Most popular questions from this chapter

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