the probability of a positive HIV test is 90%, if the person is infected, and 10% if the person is not infected. assume 1% of the population is infected. 1) find the probability a person chosen at random tests is positive ?
2) find the probability that person who tests positive is infected

Question

the probability of a positive HIV test is 90%, if the person is infected, and 10% if the person is not infected. assume 1% of the population is infected. 1) find the probability a person chosen at random tests is positive ?
2) find the probability that person who tests positive is infected

anonymous · Answer

The probability that a random person is infected is 1/100, and the probability for that person to show positive is 90/100, so we have a probability of 1/100*90/100 of a positive test ona an infected person.
The probability that a random person isn't infected is 99/100, and the probability for that person to show positive is 10/100, so we have a probability of 99/100*10/100 of a positive test ona an infected person.
The total probability of having a positive is 1/100*90/100+99/100*10/100=0.108

anonymous · Answer

thanks