Question

A medical researcher administers an experimental medical treatment to 300 patients. The patients in the study are categorized by blood types A, B, AB, and O. The researcher observed that the treatment had a favorable outcome for 63 of the 90 patients with blood type A, 31 of the 124 patients with blood type B, 6 of the 6 patients with blood type AB, and none of the 80 patients with blood type O. Use this information to complete parts (a) through (d).a) Determine the empirical probability of a favorable outcome for those patients with blood type A.P(favorable A)= nothing (Type an integer or decimal rounded to the nearest hundredth as needed.)b) Determine the empirical probability of a favorable outcome for those patients with blood type B.P(favorable B)= nothing (Type an integer or decimal rounded to the nearest hundredth as needed.)c) Determine the empirical probability of a favorable outcome for those patients with blood type AB.P(favorable AB)= nothing (Type an integer or decimal rounded to the nearest hundredth as needed.)d) Determine the empirical probability of a favorable outcome for those patients with blood type O.P(favorable O)= nothing (Type an integer or decimal rounded to the nearest hundredth as needed.)

Answer 1

We have to determine the empirical (frequentist) probability of each of the blood types.

We have a treatment with a total of 300 patients.

The outcome we get out of the experiment is:

- Blood type A: 63 positives out of 90.

- Blood type B: 31 positives out of 124.

- Blood type AB: 6 positives out of 6.

- Blood type O: 0 positives out of 80.

The probability for each group can be estimated as the ratio between the positive outcomes and the total of each blood type.

Blood type A:

$P_A(\text{favorable})=\frac{63}{90}=0.70$

Blood type B:

$P_B(\text{favorable})=\frac{31}{124}=0.25$

Blood type AB:

$P_{AB}(\text{favorable})=\frac{6}{6}=1$

Blood type O:

$P_O(\text{favorable})=\frac{0}{80}=0$

Answer:

a) 0.70

b) 0.25

c) 1

d) 0