Bayes theorem and probability help

[hoddo]

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..

 

[danago]

Perhaps try drawing a tree diagram to help represent the situation.

 

[hoddo]

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

 

[danago]

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?

 

[hoddo]

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