People with O-negative blood type are universal donors, i.e., they can donate blood to individuals with any blood type. Only 8% of people have O-negative blood. One person randomly appears to give blood. What is the probaliblity that the person does not hvae O-negative blood? Two people appear indpendently to give blood. What is the probaliblity that: Both have O-negative blood; at least one of them has O-negative blood; only one of them has O-negative blood?

Let's break down the probabilities step by step.

### 1. **Probability that the person does not have O-negative blood**
- The probability that a person **has** O-negative blood is \( P(O^{-}) = 0.08 \) (since 8% of people have O-negative blood).
- Therefore, the probability that a person **does not have** O-negative blood is:
  \[
  P(\text{not } O^{-}) = 1 - P(O^{-}) = 1 - 0.08 = 0.92
  \]

### 2. **Two people appear independently to give blood:**

#### (a) **Probability that both have O-negative blood**
- Since the two people are independent, the probability that both have O-negative blood is the product of the individual probabilities:
  \[
  P(\text{both have } O^{-}) = P(O^{-}) \times P(O^{-}) = 0.08 \times 0.08 = 0.0064
  \]

#### (b) **Probability that at least one of them has O-negative blood**
- To find the probability that **at least one** person has O-negative blood, we can use the complement rule. The complement is that neither of them has O-negative blood.
- The probability that **neither** person has O-negative blood is:
  \[
  P(\text{neither has } O^{-}) = P(\text{not } O^{-}) \times P(\text{not } O^{-}) = 0.92 \times 0.92 = 0.8464
  \]
- Therefore, the probability that **at least one** person has O-negative blood is:
  \[
  P(\text{at least one has } O^{-}) = 1 - P(\text{neither has } O^{-}) = 1 - 0.8464 = 0.1536
  \]

#### (c) **Probability that only one of them has O-negative blood**
- The probability that the **first** person has O-negative blood and the second does not is:
  \[
  P(O^{-}) \times P(\text{not } O^{-}) = 0.08 \times 0.92 = 0.0736
  \]
- Similarly, the probability that the **second** person has O-negative blood and the first does not is also:
  \[
  P(\text{not } O^{-}) \times P(O^{-}) = 0.92 \times 0.08 = 0.0736
  \]
- So, the total probability that only one of them has O-negative blood is:
  \[
  P(\text{only one has } O^{-}) = 0.0736 + 0.0736 = 0.1472
  \]

### Summary of results:
1. Probability that a person does **not** have O-negative blood: \( 0.92 \)
2. Probability that **both** have O-negative blood: \( 0.0064 \)
3. Probability that **at least one** has O-negative blood: \( 0.1536 \)
4. Probability that **only one** has O-negative blood: \( 0.1472 \)

Would you like further clarification on any part of the solution?

#### Related Questions:
1. What is the probability that three people all have O-negative blood?
2. What is the probability that none of three people have O-negative blood?
3. If four people appear, what is the probability that exactly two of them have O-negative blood?
4. How does the probability change if 12% of the population has O-negative blood?
5. What if the second person’s blood type depends on the first person’s blood type?

#### Tip:
For problems involving "at least one" probabilities, using the complement rule (1 minus the probability of the complement event) is often much simpler than calculating directly!

People with O-negative blood type are universal donors, i.e., they can donate blood to individuals with any blood type. Only 8% of people have O-negative blood. One person randomly appears to give blood. What is the probability that the person does not have O-negative blood? Two people appear independently to give blood. What is the probability that: Both have O-negative blood; at least one of them has O-negative blood; only one of them has O-negative blood?

Calculate the probability that a random person does not have O-negative blood. This problem also explores probabilities of independent events, such as two people both having O-negative blood, at least one having O-negative blood, and only one having O-negative blood. Suitable for high school students learning probability.

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