# What Is the Probability a Cow Has BSE Given a Positive Test?

• Vendatte
In summary, Bayes Rule Probability Problem is a mathematical formula used to determine the probability of an event occurring based on prior knowledge of related conditions or factors. It is commonly used in fields such as statistics, machine learning, and artificial intelligence to update the probability of an event as new evidence or information becomes available. The formula for Bayes Rule Probability Problem is P(A|B) = [P(B|A) * P(A)] / P(B), where P(A|B) is the probability of event A occurring given that event B has occurred, P(B|A) is the probability of event B occurring given that event A has occurred, and P(A) and P(B) are the individual probabilities of events A and B occurring.
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## Homework Statement

Event B is cow has BSE
Event T is the test for BSE is positive
P(B) = 1.3*10^-5
P(T|B) = .70
probability that the test is positive, given that the cow has BSE
P(T|Bcc) = .10
probability that the test is positive given that the cow does not have BSE
Find P(B|T) and P(B|Tc)
probability that the cow has BSE given that the test is positive, and probability that the cow has BSE given that the test is negative

## Homework Equations

P(Ci|A) = P(A|Ci)/P(A) = P(A|Ci) / (P(A|C1)P(C1)+P(A|C2)*P(C2) ... + P(A|Cm)*P(Cm)

## The Attempt at a Solution

The equation I use to find P(B|T) is

P(B|T) = P(T|B) / (P(T|B)*P(B)+P(T|BC)*P(Bc)

plugging in the values, I get P(B|T) = .70/(.70*(1.3*10^-5) + .1(1-(1.3*10^-5))), however that value is close to 7, which is clearly wrong.

To find P(B|Tc I plan on using the equation P(B) = P(B|T)P(T)+P(B|Tc)*P(Tc)

Any help would be greatly appreciated.

it is important to use accurate and precise calculations to determine probabilities. In this case, we are dealing with conditional probabilities which require us to consider both the likelihood of the event occurring and the prior probability of the event.

To solve for P(B|T), we can use Bayes' Theorem which states that P(B|T) = P(T|B)P(B)/P(T). Plugging in the given values, we have P(B|T) = .70*(1.3*10^-5)/(.70*(1.3*10^-5) + .1*(1-(1.3*10^-5))). This gives us a more reasonable value of approximately 0.0000902, which is the probability that the cow has BSE given that the test is positive.

To solve for P(B|Tc), we can use the equation P(B|Tc) = P(Tc|B)P(Bc)/P(Tc). Plugging in the values, we have P(B|Tc) = .10*(1-(1.3*10^-5))/(.10*(1-(1.3*10^-5)) + .70*(1.3*10^-5)). This gives us a value of approximately 0.99991, which is the probability that the cow has BSE given that the test is negative.

It is important to note that these calculations are based on the given probabilities and do not necessarily reflect the true probability of a cow having BSE or the accuracy of the test. it is important to continuously evaluate and improve upon these calculations by considering new evidence and data.

## 1. What is Bayes Rule Probability Problem?

Bayes Rule Probability Problem, also known as Bayes' theorem or Bayes' law, is a mathematical formula that determines the probability of an event occurring based on prior knowledge of related conditions or factors.

## 2. How is Bayes Rule Probability Problem used?

Bayes Rule Probability Problem is used to update the probability of an event occurring as new evidence or information becomes available. It is commonly used in fields such as statistics, machine learning, and artificial intelligence.

## 3. What is the formula for Bayes Rule Probability Problem?

The formula for Bayes Rule Probability Problem is: P(A|B) = [P(B|A) * P(A)] / P(B), where P(A|B) is the probability of event A occurring given that event B has occurred, P(B|A) is the probability of event B occurring given that event A has occurred, and P(A) and P(B) are the individual probabilities of events A and B occurring.

## 4. Can Bayes Rule Probability Problem be applied to real-life situations?

Yes, Bayes Rule Probability Problem can be applied to real-life situations where there is uncertainty or incomplete information. It can be used to make predictions or decisions based on available data and can be updated as new information is gathered.

## 5. What are the limitations of Bayes Rule Probability Problem?

Bayes Rule Probability Problem relies on the assumption that the prior probabilities and conditional probabilities are accurate, which may not always be the case in real-life situations. It also requires a large amount of data to accurately estimate probabilities, which may not always be available.

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