Question

please need some help on tree diagrams probability thank you
The test done to determine if someone is HIV positive are called enzyme immunoassay or EIA tests. The test screen a blood sample for the presence of antibodies to HIV. Like most tests, this test is not perfect. The table below shows the approximate probabilities of positive and negative EIA tests when the blood does and does not actually contain the HIV antibodies. Long range studies have shown that only 2% of the population actually has the HIV antibodies.
Test Result Positive negative
Antibodies Present 0.9985 0.0015
Antibodi

Answer 1

The test done to determine if someone is HIV positive are called enzyme immunoassay or EIA tests. The test screen a blood sample for the presence of antibodies to HIV. Like most tests, this test is not perfect. The table below shows the approximate probabilities of positive and negative EIA tests when the blood does and does not actually contain the HIV antibodies. Long range studies have shown that only 2% of the population actually has the HIV antibodies.

Test Result Positive negative
Antibodies Present 0.9985 0.0015
Antibodies Not Present 0.006 0.994

A) Explain in context all four values in the table. That is what does each of them actually mean?
Construct a tree diagram to answer the following questions. The first two choices of the tree should be whether or not the antibodies are present. The second choice be the test result.( what is the probability split for the first choices?)
B) what is the probability that a person with HIV will have a test come out positive( false-positive )
C) what is the probability that a person with HIV will have a test come out negative ( false negative )
D) what is the probability that a person with HIV will have a test come out positive



The A.P. Statistics exam consists of a multiple-choice section in which each question has five choices. Sara estimates that she has a 75% chance of knowing each question. If she does not know the answer, she will randomly guess.

a) What is the probability of Sara getting a question correct?
b) The A.P. exam has 40 questions, how many might Sara expect to get correct?

Answer 2

\(\large
\begin{array}{|l|c|}
\hline
Test Result&Positive&Negative\\
\hline
Antibodies ~Present&0.9985&0.0015\\
\hline
Antibodies~Not~Present&0.006&0.994\\
\hline
\end{array}
\)

Answer 3

start by drawing the probability tree

Answer 4

Long range studies have shown that only 2% of the population actually has the HIV antibodies.

Answer 5

that means 2% chance for having HIV antibodies present,
and 98% chance for having HIV antibodies NOT present

right ?

Answer 6

see if the probability tree makes more or less sense

Answer 7

Yes it makes more sense
For A am i suppose to explain each number like 0.9985 is the result of a person with HIV positive 0.0015 the result person that has antibodies present chance of the test becoming negative

Answer 8

Would B) Is suppose the be the probability without HIV will have a test come out true. Will the answer be 0.006? C) .0015 D) 0.9985

Answer 9

I'll get u started on part A :
\(0.9985\) : Given a person really have Antibodies Present, the \(probability\) that the Test Result to Correctly identify him as positive is 0.9985

Answer 10

similarly u can explain all other numbers, okay ?

Answer 11

okay

Answer 12

B) what is the probability that a person with OUT HIV will have a test come out positive( false-positive )

\(0.006\) is correct!

Answer 13

C and D are also right ! good job !!

Answer 14

Thank you. And thanks for the help

Answer 15

yw