How to find conditional probability, given parent node and child node
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Currently I am working on a sample question for my course:
Calculate P(Sprinkler | Cloudy=True, WetGrass=True)
based on this simple Bayesian Network diagram.
My process is as follows:
- Given the conditional probability table of Sprinkler, we can deduce P(Sprinkler) = 0.10 since we know Cloudy=True
- Since Cloudy is a parent of Sprinkler, P(Sprinker) depends on its value
- Since WetGrass is a child of Sprinkler, Sprinkler is conditionally independent of WetGrass (the former's value does not depend on the latter)
- Thus, we deduce P(Sprinker|Cloudy,WetGrass) = P(Sprinkler|Cloudy) = 0.10
When I checked the instructor's solution to this sample question, it was around 0.13. Could someone help guide me towards the correct way to approach this? I'm new to this concept, and thoroughly confused.
probability independence conditional-probability bayes-theorem bayesian-network
asked Nov 15 at 19:07
user5482356
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up vote
0
down vote
favorite
Currently I am working on a sample question for my course:
Calculate P(Sprinkler | Cloudy=True, WetGrass=True)
based on this simple Bayesian Network diagram.
My process is as follows:
- Given the conditional probability table of Sprinkler, we can deduce P(Sprinkler) = 0.10 since we know Cloudy=True
- Since Cloudy is a parent of Sprinkler, P(Sprinker) depends on its value
- Since WetGrass is a child of Sprinkler, Sprinkler is conditionally independent of WetGrass (the former's value does not depend on the latter)
- Thus, we deduce P(Sprinker|Cloudy,WetGrass) = P(Sprinkler|Cloudy) = 0.10
When I checked the instructor's solution to this sample question, it was around 0.13. Could someone help guide me towards the correct way to approach this? I'm new to this concept, and thoroughly confused.
probability independence conditional-probability bayes-theorem bayesian-network
asked Nov 15 at 19:07
user5482356
11
New contributor
user5482356 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Currently I am working on a sample question for my course:
Calculate P(Sprinkler | Cloudy=True, WetGrass=True)
based on this simple Bayesian Network diagram.
My process is as follows:
- Given the conditional probability table of Sprinkler, we can deduce P(Sprinkler) = 0.10 since we know Cloudy=True
- Since Cloudy is a parent of Sprinkler, P(Sprinker) depends on its value
- Since WetGrass is a child of Sprinkler, Sprinkler is conditionally independent of WetGrass (the former's value does not depend on the latter)
- Thus, we deduce P(Sprinker|Cloudy,WetGrass) = P(Sprinkler|Cloudy) = 0.10
When I checked the instructor's solution to this sample question, it was around 0.13. Could someone help guide me towards the correct way to approach this? I'm new to this concept, and thoroughly confused.
probability independence conditional-probability bayes-theorem bayesian-network
asked Nov 15 at 19:07
user5482356
11
New contributor
user5482356 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Currently I am working on a sample question for my course:
Calculate P(Sprinkler | Cloudy=True, WetGrass=True)
based on this simple Bayesian Network diagram.
My process is as follows:
- Given the conditional probability table of Sprinkler, we can deduce P(Sprinkler) = 0.10 since we know Cloudy=True
- Since Cloudy is a parent of Sprinkler, P(Sprinker) depends on its value
- Since WetGrass is a child of Sprinkler, Sprinkler is conditionally independent of WetGrass (the former's value does not depend on the latter)
- Thus, we deduce P(Sprinker|Cloudy,WetGrass) = P(Sprinkler|Cloudy) = 0.10
When I checked the instructor's solution to this sample question, it was around 0.13. Could someone help guide me towards the correct way to approach this? I'm new to this concept, and thoroughly confused.
probability independence conditional-probability bayes-theorem bayesian-network
probability independence conditional-probability bayes-theorem bayesian-network
asked Nov 15 at 19:07
user5482356
11
New contributor
user5482356 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 15 at 19:07
user5482356
11
New contributor
user5482356 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Nov 15 at 20:02
asked Nov 15 at 19:07
user5482356
11
New contributor
user5482356 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 15 at 19:07
user5482356
11
asked Nov 15 at 19:07
user5482356
11
11
New contributor
user5482356 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
user5482356 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
user5482356 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
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