Math  /  Data & Statistics

QuestionA medical researcher administers an experimental medical treatment to 200 patients. The patients in the study are categorized by blood types A,B,ABA, B, A B, and OO. The researcher observed that the treatment had a favorable outcome for 35 of the 50 patients with blood type A,17A, 17 of the 68 patients with blood type B,12B, 12 of the 12 patients with blood type ABA B, and none of the 70 patients with blood type OO. 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(\mathrm{P}( favorable A)=0.7)=0.7 (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(P( favorable B)=B)= \square (Type an integer or decimal rounded to the nearest hundredth as needed.)

Studdy Solution

STEP 1

What is this asking? We're figuring out how likely the treatment works for people with different blood types based on the results of a study. Watch out! Don't mix up the number of people with a certain blood type with the total number of people in the study.

STEP 2

1. Calculate Probability for Blood Type B

STEP 3

To find the probability of a favorable outcome for patients with blood type B, we'll divide the number of patients with blood type B who had a favorable outcome by the total number of patients with blood type B.
This is how we define empirical probability!
It's like figuring out how likely something is to happen based on what we've actually seen.

STEP 4

We know that **17** out of **68** patients with blood type B had a favorable outcome.
So, our calculation looks like this: P(favorable B)=Number of favorable outcomes for BTotal number of B=1768 \text{P(favorable B)} = \frac{\text{Number of favorable outcomes for B}}{\text{Total number of B}} = \frac{17}{68}

STEP 5

Now, let's crunch the numbers!
Dividing 17 by 68 gives us: 1768=0.25 \frac{17}{68} = 0.25 So, the **empirical probability** of a favorable outcome for patients with blood type B is **0.25**.

STEP 6

a) The empirical probability of a favorable outcome for patients with blood type A is 0.70.7. b) The empirical probability of a favorable outcome for patients with blood type B is 0.250.25.

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