A automotive warning light comes on when either the engine b

A automotive warning light comes on when either the engine becomes too hot or the coolant level falls too low. Assuming that these two events happen independently, with (equal) probability .1, and that the warning light is itself potentially faulty so that it turns on with probability .9 when both events are true, .8 when either one is true, and .1 when neither is true. Yon notice that the warning light is on. What is the probability your coolant is low? In subsequently checking the engine, you verify that it is indeed too hot. Given this new fact as well, what is the probability your coolant is also low?

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