Question

the table shows the blood types of 75 donors after a one - day blood drive. based on the results, what is the chance that a random donor has type a blood?

blood type	o	a	b	ab

options: \\(\frac{11}{25}\\), \\(\frac{31}{75}\\), 33, \\(\frac{7}{15}\\)

Explanation:

Step1: Recall probability formula

The probability of an event is the number of favorable outcomes divided by the total number of possible outcomes. For this problem, the favorable outcomes are the number of donors with type A blood, and the total number of possible outcomes is the total number of donors.

Step2: Identify values

From the table, the number of donors with type A blood (favorable outcomes) is 33, and the total number of donors (total outcomes) is 75.

Step3: Calculate probability

Using the probability formula \( P(\text{Type A})=\frac{\text{Number of Type A donors}}{\text{Total number of donors}} \), we substitute the values: \( P(\text{Type A}) = \frac{33}{75} \). We can simplify this fraction by dividing both the numerator and the denominator by 3: \( \frac{33\div3}{75\div3}=\frac{11}{25} \). Wait, but let's check the options. Wait, maybe I made a mistake. Wait, the number of type A donors is 33, total is 75. Wait, \( \frac{33}{75} \) simplifies to \( \frac{11}{25} \) (since 33 ÷ 3 = 11, 75 ÷ 3 = 25). Let's check the options: the first option is \( \frac{11}{25} \), the second is \( \frac{31}{75} \), third is 33, fourth is \( \frac{7}{15} \). Wait, let's recalculate: 33 divided by 75. Let's divide numerator and denominator by 3: 33/3=11, 75/3=25. So \( \frac{11}{25} \) is equivalent to \( \frac{33}{75} \). Wait, but let's check the options again. Wait, maybe I misread the table. Wait, the table says Frequency for A is 33, total donors is 75. So probability is 33/75 = 11/25. Let's check the options: the first option is \( \frac{11}{25} \), so that's the correct one? Wait, but let's check the calculation again. 33 divided by 75: divide numerator and denominator by 3: 11/25. Yes. So the correct answer should be \( \frac{11}{25} \). Wait, but let's check the options. The first option is \( \frac{11}{25} \), so that's the answer.

Wait, maybe I made a mistake in the initial thought. Let's re-express:

Probability = (Number of A donors) / (Total donors) = 33 / 75. Simplify 33/75: GCD of 33 and 75 is 3. 33 ÷ 3 = 11, 75 ÷ 3 = 25. So 11/25. So the first option is \( \frac{11}{25} \), which is the simplified form of 33/75.

Answer:

\(\frac{11}{25}\) (corresponding to the first option: \(\frac{11}{25}\))