Bayes theorem and probability help

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Homework Help Overview

The problem involves a scenario with a car's dashboard warning light related to oil pressure, focusing on the application of Bayes' theorem and probability concepts. The original poster presents a situation where the light may flash correctly or incorrectly, and they seek to determine the probability of needing to be concerned when the light activates.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the potential use of a tree diagram to visualize the problem. Questions arise regarding the interpretation of the probabilities provided, particularly how they can sum to more than 1, leading to clarification about the different cases represented by the probabilities.

Discussion Status

The discussion is ongoing, with participants exploring the setup of the problem and clarifying the meaning of the probabilities involved. Some guidance has been offered regarding the interpretation of the flashing probabilities in relation to the conditions of the oil pressure.

Contextual Notes

There is a mention of the original poster's difficulty in starting the problem, as well as concerns about the interpretation of the probabilities that exceed 100% when combined.

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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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