Bayes' Theorem- drug screening The national flufferball association decides to implement a drug screening procedure to...

Bayes' Theorem- drug screening

The national flufferball association decides to implement a drug screening procedure to test its athletes for illegal performance enhancing drugs. 3% of the professional flufferball players actually use performance enhancing drugs. A test for the drugs has a false positive rate of 2% and a false negative rate of 4%. In other words, a person who does not take the drugs will test positive with probability 0.02. A person who does take the drugs will test negative with probability 0.04. A randomly selected player is tested and tests positive. What is the probability that she really does take performance enhancing drugs?

Expert Solution

Please find the solution in attached images.

venereology answered 1 week ago

4. Bayes Theorem - One way of thinking about Bayes theorem is that it converts a-priori...

4. Bayes Theorem - One way of thinking about Bayes theorem is that it converts a-priori probability to a-posteriori probability meaning that the probability of an event gets changed based upon actual observation or upon experimental data. Suppose you know that there are two plants that produce helicopter doors: Plant 1 produces 1000 helicopter doors per day and Plant 2 produces 4000 helicopter doors per day. The overall percentage of defective helicopter doors is 0.01%, and of all defective helicopter...

4. Bayes Theorem - One way of thinking about Bayes theorem is that it converts a-priori...

4. Bayes Theorem - One way of thinking about Bayes theorem is that it converts a-priori probability to a-posteriori probability meaning that the probability of an event gets changed based upon actual observation or upon experimental data. Suppose you know that there are two plants that produce helicopter doors: Plant 1 produces 1000 helicopter doors per day and Plant 2 produces 4000 helicopter doors per day. The overall percentage of defective helicopter doors is 0.01%, and of all defective helicopter...

When is the Bayes' rule (not the Bayes' theorem) optimal? Explain the meaning of that by...

When is the Bayes' rule (not the Bayes' theorem) optimal? Explain the meaning of that by using a 2x2 confusion matrix

1. What is dependent and independent event. 2. What is the relevance of Bayes theorem in...

1. What is dependent and independent event. 2. What is the relevance of Bayes theorem in posterior probability? 3. what is the difference between discrete and continuous probability distributions?

A software company is trying to use Bayes Theorem and other rules of probability to develop...

A software company is trying to use Bayes Theorem and other rules of probability to develop an algorithm that can effectively filter out spam emails. The company’s software developers carefully examined a random sample of 5,000 emails received by its employees and found out that 1200 of the emails were spam. A closer look at the spam emails revealed that 300 of them contained the word ‘free’ in the subject line. On the other hand, only 228 of the non-spam...

A software company is trying to use Bayes Theorem and other rules of probability to develop...

A software company is trying to use Bayes Theorem and other rules of probability to develop an algorithm that can effectively filter out spam emails. The company’s software developers carefully examined a random sample of 20,000 emails received by its employees and found out that 4,400 of the emails were spam. A closer look at the spam emails revealed that 1,100 of them contained the word ‘free’ in the subject line. On the other hand, only 780 of the non-spam...

Bayesian analysis is a probabilistic classification method based on Bayes' theorem (postulated by an English Mathematician...

Bayesian analysis is a probabilistic classification method based on Bayes' theorem (postulated by an English Mathematician named Thomas Bayes). In summary, the Bayesian theory rests on the belief that the evidence about the true state of a given problem can be expressed in term of the degree of understanding of the underlying issues. That degree of understanding can in turn be expressed in terms of probability. And based on the observation, the theorem provides the relationship between the probabilities of...

MAST (Michigan Alcohol Screening Test) is one of the screening instruments used for alcohol/drug assessments. Can...

MAST (Michigan Alcohol Screening Test) is one of the screening instruments used for alcohol/drug assessments. Can you explain me WELL about MAST? because want to understand perfectly about MAST. I also need references for it.

For high risk group screening (i.e. injection drug users) as compared to generla population screening, what...

For high risk group screening (i.e. injection drug users) as compared to generla population screening, what is the best in terms of levels of sensitivity and specificity. Explain why.

Now let's use Bayes' theorem and the binomial distribution to address a Bayesian inference question. You...

Now let's use Bayes' theorem and the binomial distribution to address a Bayesian inference question. You toss a bent coin N times, obtaining a sequence of heads and tails. The coin has an unknown bias f of coming up heads. (a) If NH heads have occurred in N tosses, what is the probability distribution of f? Assume a uniform prior P(f) = 1 and make use of the following result: integral 0 to 1 f^a (1 - f)^b df =...

Question

Bayes' Theorem- drug screening The national flufferball association decides to implement a drug screening procedure to...

Solutions

Expert Solution

Related Solutions

4. Bayes Theorem - One way of thinking about Bayes theorem is that it converts a-priori...

4. Bayes Theorem - One way of thinking about Bayes theorem is that it converts a-priori...

When is the Bayes' rule (not the Bayes' theorem) optimal? Explain the meaning of that by...

1. What is dependent and independent event. 2. What is the relevance of Bayes theorem in...

A software company is trying to use Bayes Theorem and other rules of probability to develop...

A software company is trying to use Bayes Theorem and other rules of probability to develop...

Bayesian analysis is a probabilistic classification method based on Bayes' theorem (postulated by an English Mathematician...

MAST (Michigan Alcohol Screening Test) is one of the screening instruments used for alcohol/drug assessments. Can...

For high risk group screening (i.e. injection drug users) as compared to generla population screening, what...

Now let's use Bayes' theorem and the binomial distribution to address a Bayesian inference question. You...