# Is Bayes theorem reliable?

Table of Contents

## Is Bayes theorem reliable?

As this example shows, iterating Bayes’ theorem can yield extremely precise information. But if the reliability of your test is 90 percent, which is still pretty good, your chances of actually having cancer even if you test positive twice are still less than 50 percent.

## When can we apply Bayes Theorem?

The Bayes theorem describes the probability of an event based on the prior knowledge of the conditions that might be related to the event. If we know the conditional probability , we can use the bayes rule to find out the reverse probabilities .

**What is the probability that an individual has the disease if the test is negative?**

the probability that the test result is negative (suggesting the person does not have the disease), given that the person has the disease, is only 1 percent.

**What is the probability that a person who tests positive actually has the disease?**

A certain disease has an incidence rate of 2\%. If the false negative rate is 10\% and the false positive rate is 1\%, compute the probability that a person who tests positive actually has the disease. so about 65\% of the people who test positive will have the disease.

### Where can be Bayes rule be used?

Where does the bayes rule can be used? Explanation: Bayes rule can be used to answer the probabilistic queries conditioned on one piece of evidence.

### What are the conditions for Bayes Theorem?

Formula for Bayes’ Theorem P(A|B) – the probability of event A occurring, given event B has occurred. P(B|A) – the probability of event B occurring, given event A has occurred. P(A) – the probability of event A. P(B) – the probability of event B.

**What is the probability of a randomly selected person having tuberculosis given that the test indicates tuberculosis?**

(If the test indicates a person has tuberculosis, the test is positive.) Experimentation has shown that the probability of a positive test is 0.82, given that a person has tuberculosis. The probability is 0.09 that the test registers positive, given that the person does not have tuberculosis.

**What is the probability that the person actually has heart disease?**

A particular heart disease has a prevalence of 1/1000 people. A particular heart disease has a prevalence of 1/1000 people. A test to detect this disease has a false positive rate of 5\%. This means that the probability of getting a positive results GIVEN that you do NOT have the disease (that is, p(B|notA) is .

#### What is the probability that a patient has diseases meningitis with a stiff neck?

the prior probability that any patient has a stiff neck is 1/20. That is, we expect only 1 in 5000 patients with a stiff neck to have meningitis. This is still a very small chance.

#### What is the probability of a false positive?

This means that, in a population with 1\% prevalence, only 30\% of individuals with positive test results actually have the disease. At 0.1\% prevalence, the PPV would only be 4\%, meaning that 96 out of 100 positive results would be false positives.

**How is Bayes theorem used in real life?**

Bayes’ rule is used in various occasions including a medical testing for a rare disease. With Bayes’ rule, we can estimate the probability of actually having the condition given the test coming out positive. Applying Bayes’ rule will help you analyze what you gain and what you lose by taking certain actions.