A certain virus infects one in every 200 people. A test used to detect the virus in a person is positive 85% of the time if the person has the virus and 10% of the time if the person does not have the virus. (This 10%
result is called a false positive.) Let A be the event "the person is infected and B be the event the person
tests positive".
a) Find the probability that a person has the virus given that they have tested positive, i. e. find P(AIB).
Round your answer to the nearest tenth of a percent and do not include a percent sign.
P(AB)=
b) Find the probability that a person does not have the virus given that they test negative, i. e. find
P(AB). Round your answer to the nearest tenth of a percent and do not include a percent sign.
PAB) =

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?