Question

Estudio de caso Teorema de Bayes. Las historias de casos clínicos indican que diversas enfermedades producen sistemas similares. Suponga que un conjunto particular de síntomas, que se denotarán como evento M, ocurre solo cuando se presenta cualquiera de tres enfermedades, A, B o C, (Para mayor simplicidad, supondremos que las enfermedades A, B y C son mutuamente excluyentes). Estudios realizados demuestran estas probabilidades de adquirir las tres enfermedades: P(A) = 0,02 P(B) = 0,03 P(C) = 0,4 Las probabilidades de desarrollar los síntomas M, dada una enfermedad especifica, son: P(M|A)=0,80 P(M|B)=0,97 P(M|C)=0,60 Suponiendo que una persona enferma presente los síntomas M. ¿Cuál es la probabilidad de que la persona tenga la enfermedad A?

Answer 1

Answer:  A

Explanation: Case study Bayes theorem. Case histories indicate that various diseases produce similar systems. Assume that a particular set of symptoms, which will be denoted as event M, occurs only when any of three diseases, A, B or C, occurs (For simplicity, we will assume that diseases A, B and C are mutually exclusive). Studies show these probabilities of acquiring the three diseases: P (A) = 0.02 P (B) = 0.03 P (C) = 0.4 The probabilities of developing M symptoms, given a specific disease, are: P (M | A) = 0.80 P (M | B) = 0.97 P (M | C) = 0.60 Assuming that a sick person has symptoms M. What is the probability that the person has disease A?

Answer 2

Assuming that a sick person has symptoms M, the probability that the person has disease A is; 0.8

How to apply Baye's theorem?

We are given;

Probability of Disease A; P(A) = 0.02

Probability of Disease B: P (B) = 0.03

Probability of Disease C: P (C) = 0.4.

The probabilities of developing M symptoms, given a specific disease, are:

P(M | A) = 0.80

P (M | B) = 0.97

P (M | C) = 0.60

According to Baye's theoem, assuming that a sick person has symptoms M, the probability that the person has disease A is;

P(M | A) = [P(A | M) * P(M)]/P(A)

Thus; P(M|A) = 0.8

Complete Interpretation of question is;

Assume that a particular set of symptoms, which will be denoted as event M, occurs only when any of three diseases, A, B or C, occurs (For simplicity, we will assume that diseases A, B and C are mutually exclusive). Studies show these probabilities of acquiring the three diseases: P (A) = 0.02 P (B) = 0.03 P (C) = 0.4. The probabilities of developing M symptoms, given a specific disease, are: P (M | A) = 0.80, P (M | B) = 0.97, P (M | C) = 0.60.

Assuming that a sick person has symptoms M. What is the probability that the person has disease A?

Read more about Baye's Theorem at; https://brainly.com/question/14989160

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