gijsmotmans
New member
- Joined
- Oct 17, 2023
- Messages
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Hey everyone,
The question below was an assignment I got. The answer that is given takes following variables: color of prop and color the audience member says. The answer to part c of the question was 35 % by using the bayes rule. However, I do not think this is correct, as I think it would be more correct to take the correctness of the audience member as second variable, as this does not depend on the color of the prop. Then the two variables would be independent from each other. Part c of the question would then actually be simply the probability that the audience is wrong, which is 15%, instead of accounting for the fact that the red prop is more abundant, as this does not influence the correctness of the audience member.
What am I missing here?
question
In a city known for its vibrant street performers, a street magician accidentally dropped a valuable prop during a late-night performance. Two magic shops operate in the city: one with red props and the other with yellow props. You are provided with the following information: 75% of the props used by street magicians in the city are red, and 25% are yellow. An audience member identified the lost prop as yellow. The magic council decided to assess the accuracy of the audience member’s identification given the conditions of that particular night’s performance. They concluded that the audience member correctly identified each of the two prop colours 85% of the time and made mistakes 15% of the time.
a) Draw a Bayesian network for this problem. Hint: You need only two variables: one for the prop colour and one for the what the audience member sees.
b) Define the conditional probability tables (CPTs) for each of the two nodes.
c) Given the audience information, what is the probability that the prop dropped during the performance was red? Note: You don’t necessarily need the Bayesian network to answer this. You can try to answer even if you did not manage to answer the first two questions.
The question below was an assignment I got. The answer that is given takes following variables: color of prop and color the audience member says. The answer to part c of the question was 35 % by using the bayes rule. However, I do not think this is correct, as I think it would be more correct to take the correctness of the audience member as second variable, as this does not depend on the color of the prop. Then the two variables would be independent from each other. Part c of the question would then actually be simply the probability that the audience is wrong, which is 15%, instead of accounting for the fact that the red prop is more abundant, as this does not influence the correctness of the audience member.
What am I missing here?
question
In a city known for its vibrant street performers, a street magician accidentally dropped a valuable prop during a late-night performance. Two magic shops operate in the city: one with red props and the other with yellow props. You are provided with the following information: 75% of the props used by street magicians in the city are red, and 25% are yellow. An audience member identified the lost prop as yellow. The magic council decided to assess the accuracy of the audience member’s identification given the conditions of that particular night’s performance. They concluded that the audience member correctly identified each of the two prop colours 85% of the time and made mistakes 15% of the time.
a) Draw a Bayesian network for this problem. Hint: You need only two variables: one for the prop colour and one for the what the audience member sees.
b) Define the conditional probability tables (CPTs) for each of the two nodes.
c) Given the audience information, what is the probability that the prop dropped during the performance was red? Note: You don’t necessarily need the Bayesian network to answer this. You can try to answer even if you did not manage to answer the first two questions.
