Understanding Bayes Theorem with an Example: 0.72 or 0.28?

In summary, according to Bayes' theorem, the probability of the image being of a cat given that it is actually a cat is 0.72.
  • #1
shivajikobardan
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https://lh4.googleusercontent.com/FCqUErWAqlG8w0CskhcsLgpG91xyxzAkV_nD-bZAq8147-_RKesQDpglwqF5ylKZ0Q6VW88jX-KNuIpSXi9vhw5AiWmwiv_fMyyUo_WWZJG4uwWS0aB-3rGMA0h0PDo7ZpolexCe
this is the question



Here is a tutorial video but his steps are very confusing to me. I personally know bayes theorem and have already studied probability and got good marks in it(It may not be a metric for being quality in it given that it is nepal we are talking about.)
https://courses.engr.illinois.edu/ece448/sp2020/slides/lec15.pdf
here is the slide I'm referring to. The answer seems 0.72 or 0.28 according to video.
 
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  • #2
The answer is 0.72. The formula for Bayes' theorem is P(A|B) = (P(B|A) * P(A)) / P(B), where P(A) and P(B) are the probabilities of events A and B, respectively, and P(A|B) is the probability of event A given that event B has already occurred. In this case, P(A) is the probability of it being a cat (0.72), P(B) is the probability of the image being of a cat (1), and P(B|A) is the probability of the image being of a cat given that it is actually a cat (1). Therefore, P(A|B) = (1 * 0.72) / 1 = 0.72.
 

Related to Understanding Bayes Theorem with an Example: 0.72 or 0.28?

What is Bayes Theorem and how does it work?

Bayes Theorem is a mathematical formula that helps us calculate the probability of an event occurring based on prior knowledge or information. It works by using conditional probabilities, which take into account the probability of one event occurring given that another event has already occurred.

What is an example of Bayes Theorem in action?

One example of Bayes Theorem is predicting the likelihood of a person having a certain disease based on their symptoms and the prevalence of the disease in the population. This can be helpful in medical diagnostics and decision-making.

What does the 0.72 or 0.28 represent in the example?

In Bayes Theorem, the numbers 0.72 and 0.28 represent the probabilities of the event occurring (0.72) and not occurring (0.28) respectively. These are also known as prior probabilities, which are based on existing knowledge or information before new data is taken into account.

How is Bayes Theorem useful in real-world applications?

Bayes Theorem can be applied in various fields such as medicine, finance, and artificial intelligence. It helps us make more accurate predictions and decisions by taking into account both prior knowledge and new data or evidence.

What are some limitations of Bayes Theorem?

Bayes Theorem relies on the accuracy and completeness of prior knowledge, which may not always be available or reliable. It also assumes that events are independent of each other, which may not always be the case in real-world scenarios. Additionally, it can become computationally challenging when dealing with multiple variables and complex data.

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