A country has a population of 21M people. Some people received a certain treatmentand some didn’t. Table 1 shows the disease rates based on age and treatment status.The treatment has no side effects, and only changes the probability that someonecontracts this (undesirable) disease.Age Untreated TreatedPeople Disease Disease per 100K People Disease Disease per 100Kyoung 5,000,000 40 0.8 5,000,000 20 0.4old 1,000,000 60 6.0 10,000,000 300 3.0Table 1: Disease rates based on age and treatment status.(a) Define the following events and compute four conditional probabilities of contract-ing the disease based on a person’s age and based on their treatment status. The eventsare D:= contracting the disease, Y := young, O:= old, T:= treated, and U:=untreated.Note that O = Y c, and similarly for T and U. Now, calculate 4 probabilities likeP(D|T, Y ) for each possibility.(b) What is the probability of contracting the disease if you are treated? Untreated?(c) Based on the results from (a) and (b) should a person receive the treatment if theywish to avoid contracting the disease? Does your answer change if they are young orold? Provide and explain for the apparent contradiction. A country has a population of 21M people. Some people received a certain treatmentand some didn't. Table shows the disease rates based on age and treatment status.The treatment has no side effects, and only changes the probability that someonecontracts this (undesirable) disease.Ageyoung 5,000,000old1,000,000UntreatedPeople Disease Disease40607. The below questper 100K0.86.0TreatedPeople Disease Disease per 100K5,000,0000.410,000,0003.0Table 1: Disease rates based on age and treatment status.(a) Define the following events and compute four conditional probabilities of contract-ing the disease based on a person's age and based on their treatment status. The eventsare D:= contracting the disease, Y:= young, O:= old, T:= treated, and U:=untreated.Note that O = Y, and similarly for T and U. Now, calculate 4 probabilities likeP(DT, Y) for each possibility.20300(b) What is the probability of contracting the disease if you are treated? Untreated?(c) Based on the results from (a) and (b) should a person receive the treatment if theywish to avoid contracting the disease? Does your answer change if they are young orold? Provide and explain for the apparent contradiction.Chapter 2. Exercise 7.

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A First Course in Probability (10th Edition)

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Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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A country has a population of 21M people. Some people received a certain treatment and some didn’t. Table 1 shows the disease rates based on age and treatment status. The treatment has no side effects, and only changes the probability that someone contracts this (undesirable) disease. Age Untreated Treated People Disease Disease per 100K People Disease Disease per 100K young 5,000,000 40 0.8 5,000,000 20 0.4 old 1,000,000 60 6.0 10,000,000 300 3.0 Table 1: Disease rates based on age and treatment status. (a) Define the following events and compute four conditional probabilities of contract- ing the disease based on a person’s age and based on their treatment status. The events are D:= contracting the disease, Y := young, O:= old, T:= treated, and U:=untreated. Note that O = Y c, and similarly for T and U. Now, calculate 4 probabilities like P(D|T, Y ) for each possibility. (b) What is the probability of contracting the disease if you are treated? Untreated? (c) Based on the results from (a) and (b) should a person receive the treatment if they wish to avoid contracting the disease? Does your answer change if they are young or old? Provide and explain for the apparent contradiction.

A country has a population of 21M people. Some people received a certain treatment
and some didn't. Table shows the disease rates based on age and treatment status.
The treatment has no side effects, and only changes the probability that someone
contracts this (undesirable) disease.
Age
young 5,000,000
old
1,000,000
Untreated
People Disease Disease
40
60
7. The below quest
per 100K
0.8
6.0
Treated
People Disease Disease per 100K
5,000,000
0.4
10,000,000
3.0
Table 1: Disease rates based on age and treatment status.
(a) Define the following events and compute four conditional probabilities of contract-
ing the disease based on a person's age and based on their treatment status. The events
are D:= contracting the disease, Y:= young, O:= old, T:= treated, and U:=untreated.
Note that O = Y, and similarly for T and U. Now, calculate 4 probabilities like
P(DT, Y) for each possibility.
20
300
(b) What is the probability of contracting the disease if you are treated? Untreated?
(c) Based on the results from (a) and (b) should a person receive the treatment if they
wish to avoid contracting the disease? Does your answer change if they are young or
old? Provide and explain for the apparent contradiction.
Chapter 2. Exercise 7.

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