Only 3% of a population carries the virus of a contagious disease. There is medical test to identify the virus, which identify with a 97% success rate among the virus-carriers. On the other hand, it can identify correctly among the non-carriers 94% of time.
1.) What is the probability that a randomly chosen person will be tested positive for the virus?
2.) If a randomly selected person is tested positive for the virus, what is the probability that the person is actually carrying the virus?