Questions: There are four major blood types, A, B, O, and AB. Each of these blood types may contain what is called the rhesus antigen. The presence of the rhesus antigen is designated as Rh+; the omission of the rhesus is designated by Rh-. A sample of population and the presence of a blood type is given in the table below. Type A B O AB Total Rh+ 180 50 180 15 425 Rh- 25 10 35 5 75 Total 205 60 215 20 500 (a) If a person is selected from this group, what is the probability that person has blood type O ? (Enter your probability as a fraction.) (b) If a person is selected from this group, what is the probability that person is Rh+ ? (Enter your probability as a fraction.) (c) If a person is selected from this group, what is the probability that person has blood type AB and is Rh-? (Enter your probability as a fraction.)

Solution Steps

To solve these probability questions, we need to use the basic probability formula: \[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

(a) For the probability that a person has blood type O, we need to divide the number of people with blood type O by the total number of people.

(b) For the probability that a person is Rh+, we need to divide the number of Rh+ people by the total number of people.

(c) For the probability that a person has blood type AB and is Rh-, we need to divide the number of people with blood type AB and Rh- by the total number of people.

To find the probability that a randomly selected person has blood type O, we use the formula: \[ P(O) = \frac{\text{Number of people with blood type O}}{\text{Total number of people}} = \frac{215}{500} \] This simplifies to: \[ P(O) = \frac{43}{100} \]

Next, we calculate the probability that a randomly selected person is Rh+. The formula is: \[ P(\text{Rh}^+) = \frac{\text{Number of Rh+ people}}{\text{Total number of people}} = \frac{425}{500} \] This simplifies to: \[ P(\text{Rh}^+) = \frac{17}{20} \]

Finally, we find the probability that a randomly selected person has blood type AB and is Rh-. The formula is: \[ P(\text{AB and Rh}^-) = \frac{\text{Number of AB and Rh- people}}{\text{Total number of people}} = \frac{5}{500} \] This simplifies to: \[ P(\text{AB and Rh}^-) = \frac{1}{100} \]

Final Answer