Question

In a medical study, patients are classified in 8 ways according to whether they have blood type $A B^{+}$, $A B^{-}, A^{+}, A^{-}, B^{+}, B^{-}, O^{+},$ or $O^{-},$ and also accord ing to whether their blood pressure is low, normal, or high. Find the number of ways in which a patient can be classified.

Name: Problem 22, Chapter 2: Probability and Statistics for Engineers and Scientists
Uploaded: 2021-06-03T12:13:31-08:00
Duration: 1 min 11 s
Channel: Manisha Sarker
Description: In a medical study, patients are classified in 8 ways according to whether they have blood type A B^+, A B^-, A^+, A^-, B^+, B^-, O^+, or O^-, and also accord ing to whether their blood pressure is low, normal, or high. Find the number of ways in which a patient can be classified.

   In a medical study, patients are classified in 8 ways according to whether they have blood type $A B^{+}$, $A B^{-}, A^{+}, A^{-}, B^{+}, B^{-}, O^{+},$ or $O^{-},$ and also accord ing to whether their blood pressure is low, normal, or high. Find the number of ways in which a patient can be classified.

Probability and Statistics for Engineers and Scientists

Ronald E. Walpole,… 10th Edition

Chapter 2, Problem 22

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Solved by Expert Manisha Sarker

06/03/2021

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These blood types are $A B^{+}$, $A B^{-}, A^{+}, A^{-}, B^{+}, B^{-}, O^{+},$ or $O^{-}$. Show more…

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In a medical study, patients are classified in 8 ways according to whether they have blood type $A B^{+}$, $A B^{-}, A^{+}, A^{-}, B^{+}, B^{-}, O^{+},$ or $O^{-},$ and also accord ing to whether their blood pressure is low, normal, or high. Find the number of ways in which a patient can be classified.

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Key Concepts

Independent Categories

When classifying items based on multiple independent attributes, the choices from one category do not affect the choices in another. This independence allows us to use the multiplication method to compute the total classifications, as the count of outcomes in each category can be multiplied together to yield the global number of outcomes.

Fundamental Counting Principle

This principle states that if there are several stages of a process and each stage can occur in a certain number of ways independently, the total number of ways the entire process can occur is the product of the number of ways each stage occurs. It’s essential in areas of combinatorics and probability to quickly determine the number of outcomes without listing them all.

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