The blood types of 900 people are collected at a doctor's office. The table shows the breakdown of patients by blood type. If a person from this group is selected at random, what is the probability that this person has type O blood? Express your answer as a fraction in lowest terms or as a decimal rounded to the nearest millionth (if necessary).
| Blood Type | Number of Patients |
|---|---|
| A | 275 |
| B | 265 |
| O | 275 |
| AB | 85 |
Answer (2)
The probability that a randomly selected person has type O blood is 36 11 . This fraction represents the simplest form of the probability, derived from the original count of patients with type O blood compared to the total number of patients. Alternatively, this probability can be approximated as 0.3056 in decimal form.
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Calculate the probability of a person having blood type O: 900 275 .
Simplify the fraction by dividing both the numerator and denominator by 25.
The simplified fraction is 36 11 .
The probability that a randomly selected person has type O blood is 36 11 .
Explanation
Analyze the problem We are given the blood types of 900 people and asked to find the probability that a randomly selected person has type O blood.
Determine the approach To find the probability, we need to divide the number of people with type O blood by the total number of people.
Calculate the probability The number of people with type O blood is 275, and the total number of people is 900. So, the probability is 900 275 .
Simplify the fraction Now, we simplify the fraction 900 275 by dividing both the numerator and the denominator by their greatest common divisor, which is 25.
Divide by the greatest common divisor 900 275 = 900 ÷ 25 275 ÷ 25 = 36 11
State the final answer Therefore, the probability that a randomly selected person has type O blood is 36 11 .
Examples
In healthcare, understanding the distribution of blood types within a population is crucial for managing blood supplies and planning for transfusions. For example, if a hospital knows that a certain percentage of the population has type O blood, they can better prepare for emergencies where type O blood is needed, as it is the universal donor.
