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 39 of the 130 patients with blood type a, 13 of the 26 patients with blood type b, 4 of the 4 patients with blood type ab, and none of the 140 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) = □ (type an integer or a simplified fraction.)

Explanation:

Step1: Recall the formula for empirical probability

Empirical probability \(P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\).

Step2: Identify the number of favorable outcomes and total outcomes for blood type A

The number of patients with blood type A is \(n = 130\) (total outcomes for blood - type A), and the number of patients with blood type A who had a favorable outcome is \(m=39\) (favorable outcomes for blood - type A).

Step3: Calculate the empirical probability

Using the formula \(P(\text{favorable}|A)=\frac{m}{n}\), we substitute \(m = 39\) and \(n = 130\). Then \(P(\text{favorable}|A)=\frac{39\div13}{130\div13}=\frac{3}{10}\)

Answer:

\(\frac{3}{10}\)