In the design of automobile dashboards warning lights have r

In the design of automobile dashboards, warning lights have replaced gauges. The warning lights are intended to alert drivers of impending engine problems. Let T represent the event that an engine problem occurs and L represent the event that a warning light turns on. Suppose and Assuming that use Bayes Rule to express and in terms of p and r. If a the dashboard design displays and what are the resulting values for and ?

Solution

T - engine problem occurs

R = Warning light turns on

p = probability that engine problem occurs - P(T1)

q = prob that no engine problem - P(T2)

r = prob that Warning light turns on

P(R) = P(T1R) + P(T2R) = pr +r(1-p) = r

P(T1/R) =   = p

and P(T2/R) = 1-p