I am trying to understand how to apply Bayes Theorem to solve the following question:
A drug manufacturer claims that its roadside drug test will detect the presence of cannabis in the blood 90% of the time ( i.e. show a positive test for a driver who has smoked cannabis in the last 72 hours). However, the manufacturer admits that 10% of all cannabis-free drivers also will test positive. A national survey indicates that 20% of all drivers have smoked cannabis during the last 72 hours.
What is the probability that a driver has smoked cannabis in the last 72 hours if they have tested positive?
My understanding was this:
P(A): Smoked cannabis in last 72 hours (0.20)
P(B|A): Positive test for a driver who has smoked cannabis in last 72 hours (0.9)
I don't understand how to figure out (B), which should be population tested positive. Is the figure 10% correct? It only gives false positives. Thanks.