Assume that a diagnostic test for EPM (equine protozoal myoeloencephalitis) has a sensitivity of 89% and a specifity of 92%. The prevalence of the disease is 1%
- What is the probability that a randomly selected horse will test positive on the diagnostic test if the horse is healthy?
- What is the probability that a randomly selected horse (from the total population) will test positive on the diagnostic test?
I think in 1. I have to use the definition of conditional probability (https://en.wikipedia.org/wiki/Conditional_probability the one that says Kolmogorov definition) to calculate the probability of the intersection (positive and healthy), but I'm a bit stumped on 2.
edit: I think I might have figured it out. I have to use the law of total probability, it seems. Still, I'd appreciate some feedback if possible, since I have nowhere to check if my answer is correct and I'm very new to this stuff.