Due to pollution 25 percent of the people in a country suffer from a lung related desease and 10 percent have another desease. For simplicity we assume that there are no people having both this lung related desease and another desease. It is known that 50 percent of the people infected by this lung related desease needs to be hospitalized in a hospital. From historical data it is also known that 6 percent of the population needs to be hospitalized in a hospital due to other deseases then this lung related desease Compute the probability that a person needs to be hospitalized and the condi- tional probability that a person suffer from this lung related desease given that this person is bosnitalized
Due to pollution 25 percent of the people in a country suffer from a lung related desease and 10 percent have another desease. For simplicity we assume that there are no people having both this lung related desease and another desease. It is known that 50 percent of the people infected by this lung related desease needs to be hospitalized in a hospital. From historical data it is also known that 6 percent of the population needs to be hospitalized in a hospital due to other deseases then this lung related desease Compute the probability that a person needs to be hospitalized and the condi- tional probability that a person suffer from this lung related desease given that this person is bosnitalized
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Due to pollution 25 percent of the people in a country suffer from a lung related desease and
10 percent have another desease. For simplicity we assume that there are no people having both
this lung related desease and another desease. It is known that 50 percent of the people infected
by this lung related desease needs to be hospitalized in a hospital. From historical data it is also
known that 6 percent of the population needs to be hospitalized in a hospital due to other deseases
then this lung related desease
Compute the probability that a person needs to be hospitalized and the condi-
tional probability that a person suffer from this lung related desease given that this person is
hospitalized.
The authorities do not know how many people in the country are suffering from
this lung related desease and so the above 25 percent is not based on reality. To get an
estimation of this percentage all the people in the country need to do some test to detect this
lung related desease. The type I error of this test given by P(test is negative|person has the
lung related desease ) = 0.4 and the type II error given by P(test is positive |person has
not this lung related desease) equals 0.3 Of the population taking the test 40 percent tested
positive. Observe if the test is positive this means that according to the test the person has
this lung related desease. Give an estimate of the fraction of the population having this lung
related desease.
In total the total population of the country is 100.000. Give an estimate of the
number of beds necessary in the hospital using the updated estimate derived in part 2.
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