Question

In: Statistics and Probability

In a population, 28 % of people have a disease called D, a certain kind of...

In a population, 28 % of people have a disease called D, a certain kind of skin problem, among them 42 % will develop into skin cancer. For people without this skin problem (D), only 8 % will have skin cancer.

a) What is the rate of skin cancer in this population

b) If a person found out that he has skin cancer, what is the chance that he had skin problem (D)?

Expert Solution

Let A defines an event of getting a skin disease.

A^c defines an event of not getting skin disease.

It is given that 28% of people have D-disease. Hence, P(A) = 0.28 and P(A^c) = 0.72

Let B defines an event of developing skin cancer.

Among those diseased people 42% people will develop into skin cancer. Hence, probability that people will develop skin cancer given that they have skin disease D is 0.42. Hence, P( B|A ) = 0.42

For people without skin problem, only 8% will have skin cancer. Hence, probability of having skin cancer given that the person is not having skin disease is 0.08. That is, P( B|A^c ) = 0.08

(a) - We need to find the rate of skin cancer. That is P( B )

The Law of total probability states that,

Hence, the rate of skin cancer in the population is 17.52%

(b) -

We need to find the chance that the person had a skin problem given that he has a skin cancer. That is P( A|B )

According to the Baye's theorem,

Hence, If a person found out that he has a skin cancer, there is 67.12% chance that he had skin problem.

I hope you find the solution helpful. Feel free to ask any doubt in the comment section.

Please do not forget to vote the answer. Thank you in advance!!!

orchestra answered 1 year ago

Suppose that, in an urban population, 50% of people have no exposure to a certain disease,...

Suppose that, in an urban population, 50% of people have no exposure to a certain disease, 40% are asymptomatic carriers, and 10% have the disease with symptoms. In a sample of 20 people, we are interested in the probability that the sample contains a number of asymptomatic carriers that is exactly thrice the number that have the disease with symptoms. While the final numerical answer is important, the setup of the solution is moreso.

The percentage of people in a population that get sick with a particular disease is called?...

The percentage of people in a population that get sick with a particular disease is called? Cases of an infectious disease affect a large population, beyond the localized area where it first appeared is called? Random mutations in a microbe lead to small alterations in the protein sequence of a pilus is called? A disease occurs naturally in a particular geographic location is called? A pathogen that can be used for bioterrorism is called? The disease that results when an...

The proportion of people in a given community who have a certain disease is 0.01. A...

The proportion of people in a given community who have a certain disease is 0.01. A test is available to diagnose the disease. If a person has the disease, the probability that the test will produce a positive signal is 0.95. If a person does not have the disease, the probability that the test will produce a positive signal is 0.02. a.Given that the test is positive, what is the probability that the person has the disease? b.Given that the...

Cystic fibrosis is a disease in which people have a mutation in an ion channel called...

Cystic fibrosis is a disease in which people have a mutation in an ion channel called CFTR. This type of channel is found in multiple tissues throughout the body, and a simple mutation in this channel may be expressed in a multitude of ways (sweating disorder, digestive system malfunction, respiratory difficulties, etc…). This type of situation when a genetic mutation expresses itself in a multitude of phenotypes is called Select one: a. Polygenic inheritance b. Codominance c. Epistasis d. Pleiotropy...

With a town of 20 people, 2 have a certain disease that spreads as follows: Contacts...

With a town of 20 people, 2 have a certain disease that spreads as follows: Contacts between two members of the town occurred in accordance with a Poisson process having rate ?. When contact occurs, it is equally likely to involve any of the possible pairs of people in the town. If a diseased and non-diseased person interect, then, with probability p the non-diseased person becomes diseased. Once infected, a person remains infected throughout. Let ?(?) denote the number of...

100 people are tested for disease. 30 people have the disease and 70 do not. There...

100 people are tested for disease. 30 people have the disease and 70 do not. There were 20 true positives and 37 true negatives. Part 1: What was the sensitivity of the test? Be sure to give context. Part 2: What was the specificity of the test? Be sure to give context. Part 3: What was the positive predictive value of the test? Be sure to give context. Part 4: What was the accuracy of the test? Be sure to...

The prevalence of a disease D in the population is 10%. A new test is introduced...

The prevalence of a disease D in the population is 10%. A new test is introduced by a laboratory with the following characteristics. The laboratory notes that if someone has the disease, his or her test will be positive 90% of the time (P(pos|D) = 0.90). However, a completely healthy individual will test positive with probability 0.06 (P (pos|Dc) = .06). (a) If we randomly select 5 people from this population, what is the probability that all of them...

Suppose that a test for a certain disease has a specificity of 95%. If 2,000 people...

Suppose that a test for a certain disease has a specificity of 95%. If 2,000 people without the disease take the test, how many should you expect to test negative? 100 1,000 1,500 1,900

There is 128 people with no disease and 397 with disease. Out of people with disease,...

There is 128 people with no disease and 397 with disease. Out of people with disease, 256 tested positive. Out of people with no disease, 1 tested positive. Suppose general disease probability is 0.1. What's the probability that a randomly picked person infected with the disease tests negative? (use Bayes theorem)

Disease A is autosomal dominant. A total of 4% of the study population of 100 people...

Disease A is autosomal dominant. A total of 4% of the study population of 100 people are affected. How many carriers are in the study population? Disease A is autosomal recessive. A total of 16% of the study population of 100 people are affected. How many carriers are in the study population? TIA!