Solving a Probability Problem with Bayes Theorem

In summary, the question is asking for the probability that the last ball taken out of a sack containing 5 red balls, 5 black balls, and 5 white balls is red, given that the first ball taken out is not white. This can be solved using the Bayes Theorem, the definition of conditioned probability, and the complete probability formula. The probability tree for this problem may be large, so it is helpful to start by considering different events and using the given formulas.
  • #1
ENgez
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Homework Statement


you have a sack with 5 red balls, 5 black balls and 5 white balls. you take them out one at a time without returning until the sack is empty. what is the probability the last ball you took out is red given that the first ball taken out is not white.



Homework Equations


it should be solvable using the bayes theorom, the definition of conditioned probabilty, and the complete probability formula.



The Attempt at a Solution


i tried playing around with different events and using the formulas above but no luck... the main problem is that the probability tree is huge. i was hoping i can get a push in the right direction.

thanks.
 
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  • #2
Hi ENgez! :smile:

You have a sack with 5 red balls, 4 black balls and 5 white balls. You take them out one at a time without returning until the sack is empty. what is the probability the last ball you took out is red? :wink:
 

FAQ: Solving a Probability Problem with Bayes Theorem

What is Bayes Theorem?

Bayes Theorem is a mathematical formula that helps us calculate the probability of an event happening based on prior knowledge or evidence.

How is Bayes Theorem used in probability problems?

Bayes Theorem is used to update the probability of an event occurring as new information or evidence becomes available. It is commonly used in situations where the probability of an event is affected by multiple factors or variables.

What are the key components of Bayes Theorem?

The key components of Bayes Theorem are the prior probability, likelihood, and posterior probability. The prior probability is our initial belief about the probability of an event. The likelihood is the probability of the evidence given the event. The posterior probability is the updated probability of the event after considering the new evidence.

How does Bayes Theorem differ from other probability techniques?

Bayes Theorem differs from other probability techniques because it allows us to incorporate new evidence into our calculations and update our initial beliefs. It also takes into account the relationship between multiple factors or variables, whereas other techniques may only consider one factor at a time.

What are some real-world applications of Bayes Theorem?

Bayes Theorem has many real-world applications, including medical diagnosis, spam filtering, weather forecasting, and predicting the outcome of legal cases. It is also used in machine learning and artificial intelligence algorithms.

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