Question

Consider the experiment of randomly selecting an adult American. Let A be the event that a person has the disease and let B be the event that a person tests positive for the disease.

(a) There are three probabilities given above. Give each of them in terms of the events A and B.

(b) In terms of the events A and B, what probability is it that we wish to compute? Give the correct “formula” for computing that probability

(c) Think of this experiment as a two-step process: At the first step the randomly selected person either has the disease or they don’t, and at the second step they either test positive for the disease or they don’t. Draw a tree diagram for this situation and label each of the branches with the probability of “travelling” that branch, as we have already done.

(d) Find P(B), the probability that a person tests positive for the disease. Don’t round your answer.

(e) Find the desired probability to three places past the decimal, which is the probability that you really have the disease, given that you tested positive. Do you have cause for immediate concern?

Answer 1

Here we use the conditions probability formula