statistic probability

Question

A new medical drug to cure HIV/AIDS has just been developed. The probability that it will cure HIV/AIDS is 0.9 if the patient has HIV/AIDS. The probability that it will cure HIV/AIDS falls to 0.4 if the patient does not have the disease. There is a probability of 0.3 that a person chosen at random from the community has HIV/AIDS. Find the following: i. Probability that a patient is cured of HIV/AIDS [12 Marks) Probability that a person is cured of HIV/AIDS actually had HIV/AIDS. [8 Marks)

Answer 1

I know how to do this and if you book a session, I can work with you to help you understand this better because we can discuss to find out where your difficulties are. I am going to attempt to give you guidance for this without simply giving you the answer. I am going to describe the logic behind Bayes theorem without focussing on the formula. If you work through this answer enough to understand it, I think you will find Bayes theorem is easy to understand after all!

You can use a tree diagram to illustrate the various possibilities and label each branch with the data showing how probable they are.

For example, if the probability that the random person drawn from the community has AIDS is 0.3, what is the probability that they didn't have AIDS? Review what the sum of the probability of any statement (such as Person has AIDS s and its complement (they do not) is if not sure.

Draw a tree diagram preferably with two branches extending to the right (the root of the tree on the left), one for each of those, and label each with the corresponding probability.

From each of these two "leaves" (the right-most end-points of each branch), draw two new branches, one for each possibility regarding whether or not the drug cures the patient's AIDS like symptoms..

(To make this problem a bit less ridiculous --- Let's assume that by "curing" the disease when a patient did not have the disease they meant that the person's AIDS like symptoms went away -- it is admittedly a weird thing that this problem is claiming --- a drug can cure a disease that a patient did not have? Really?!?!?)

Then the total probability of being cured is the sum of the products of the probabilities enroute from the root to each leaf in which the patient was cured. Among that set of paths that reach "Patient was cured" destination leafs, we want to know the probability that the branch we went down was the one saying the patient had AIDS. So the answer to the question would be the ratio of the product of probabilities down that branch divided by the total probability of being cured.

Make sense? Contact me through Wyzant to request an appointment. Let me know what time and day you prefer to start and what you would like to discuss. I'd be happy to give you as much feedback and guidance so that you learn how to treat these sorts of questions.