Bayes theorem and probability help

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SUMMARY

The discussion focuses on applying Bayes' theorem to determine the probability that a driver should be concerned when a dashboard warning light flashes. Given the parameters, the light flashes correctly 99% of the time when oil pressure is low, and 2% of the time when it is not. The calculated probability of concern, P(concerned), is 0.117, indicating a 11.7% chance that the oil pressure is indeed low when the light activates. This analysis illustrates the practical application of Bayes' theorem in real-world scenarios involving conditional probabilities.

PREREQUISITES
  • Understanding of Bayes' theorem
  • Familiarity with probability concepts
  • Ability to interpret conditional probabilities
  • Basic skills in constructing probability tree diagrams
NEXT STEPS
  • Study the derivation and applications of Bayes' theorem in various contexts
  • Learn how to construct and interpret probability tree diagrams
  • Explore examples of conditional probability in real-life situations
  • Investigate the implications of false positives and false negatives in probability assessments
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Students studying probability theory, data analysts working with predictive models, and anyone interested in applying statistical reasoning to real-world problems.

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Homework Statement


'A dashboard warning light is supposed to flash red if a car’s oil pressure is
too low. On a certain model, the probability of the light flashing when it should is 0.99; 2%
of the time, though, it flashes for no apparent reason. If there is a 10% chance that the oil
really is low, what is the probability that a driver needs to be concerned if the warning light
goes on?'


Homework Equations



Law of total probability/bayes theorem?


The Attempt at a Solution


having trouble making a start..
 
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Perhaps try drawing a tree diagram to help represent the situation.
 


i'm not sure how to do that though,
because of the 0.99 and the 2%,
add up to more than 1?
 


They are for different cases though, which is why it adds up to more than 100%.

The question states that IF the oil pressure is actually too low, then it will flash 99% of the time.

On the other hand though, if the oil pressure is not too low, then it will still flash 2% of the time.

Can you see how those figures are allowed to add up to more than 100%? Does that help?
 


P(concerned) = (0.99 x 0.1) + (0.02 x 0.9) = 0.117?
 

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