There are 6421 students living in Colleges of Residence at a large University. University authorities investigating the use of P among college residents sample randomly 300 college residents and ask the question: “Have you ever used P?” There are 21 responses of YES.
(a) Write down your estimate for the percentage (or proportion) of college residents who have used P.
(1 mark)
There was concern among University authorities about the truth of the response to the question and the following year a different procedure was used. A random sample of 300 college residents was again selected and the following procedure was carried out

A. Roll an unbiased six-sided die, allowing no one else to observe the outcome.
B. (I) If die shows 1, toss a fair coin and answer truthfully YES or NO to the question “Have you thrown a head?”
(ii) If die shows any other number answer truthfully YES or NO to the question “Have you ever used P?”
With this procedure, each college resident responded with a single YES or NO answer. The tree diagram is as follows where θ is the proportion of YES responses to the substance question. The problem is to find θ.

(b) Copy the tree diagram adding the four missing probabilities. (1 mark)
(c) The authorities received 84 YES responses and 216 NO responses.
(I) Write down the probability of a response YES in terms of θ. (1 mark)
(ii) Hence find the estimate, θ, for the proportion of Year 13 students who have tried P. (1 mark)
(iii) Compare this value with that obtained in (a), stating your conclusion about the proportion who have tried P. (1 mark)

Air traffic controllers are required to undergo periodic random drug testing. A urine test is used for initial screening. This test detects the presence of drugs such as amphetamines, opiates and barbiturates. Its sensitivity is 0.96 and its specificity is 0.93. Aviation authorities know from past drug testing that the probability (prevalence) of drug use by air traffic controllers at a given time is 0.007.
(I) Construct the tree diagram for this urine test, indicating the probabilities at each branch, and the four outcome probabilities.
(ii) Calculate the probability that the test is positive.
(iii) One air traffic controller returns a positive result. What is the probability this controller had used one of the drugs.

Keep this BS up and you'll probably be banned. At the very least most of your posts will be removed.

Posting the same question over and over, and inserting it into other people's active threads, is against site rules... and a good way to get everybody to ignore any legitimate question you might have.

Also... please note that site rules state we will not do your homework for you.

Its not my homework.I am trying to learn how to do probability properly and I got stuck on this question.I have been asking for help for a long time and no one has even bothered to help me so I thought maybe if I ask a question on people's thread then I will get an answer.I am very sorry for all of this but honestly I really do need help with trying to figure this problem.

Thank you for taking the time to copy your homework to AMHD.
Please refer to this announcement: https://www.askmehelpdesk.com/financ...-b-u-font.html

I have tried solving this question myself... and I don't think it is right.Ok my answer was 0.96*o.007=0.0067 and I am not sure if that is right for both questions... can you please help me!

STOP Spamming the site.
ANY re-occurrence WILL result in your removal!

Not to mention that you're posting the same stuff over in the accounting forum. I don't think "being new" makes it too tough to understand that your class is math and not accounting.

As for asking for help "for a long time" and no one "bothering" to answer... um, you might try giving it more than a half hour. We're volunteers and have lives. I tutor online for a living and even when getting paid and doing it live, we can't always get to questions that quickly! This isn't live, and perhaps no one who knows your question has gotten to it yet. Perhaps your expectations of help you are getting free are a little high.