Hint
You can use the following to help you step through the process of solving this problem. All the answer blanks in this hint are optional and are not graded.
Let $D$ be the event that the person has the disease, and let $H$ be its complement, the event $H=D^c$ that the person does not have the disease, i.e., is healthy. Let $Y$ be the event that the person tests positive for the disease, and let $N$ be its complement, the event $N=Y^c$ that the person tests negative for the disease. A first step is to translate the given data into probabilities about these events.
$P(D) = $
,
$P(H) = $
,
$P(Y \,|\, D) =$
,
$P(Y \,|\, H) =$
,
$P(N \,|\, D) =$
,
$P(N \,|\, H) =$
Are any of these quantities the probability that a person who received a positive result on the test actually has the disease?
What is the expression for this probability in terms of the events $D$, $H$, $Y$, or $N$?
To convert from the given probabilities to this probability, we need to use
' theorem.
Write the form of ＿' Theorem that we need to use to convert to $＿$.
$＿$ $=$
There should be one factor in your formula that we haven't determined yet. It is the probability
. Write a formula for $＿$ in terms of the probabilities we have defined above.
$＿$ $=$
(The formula should have two terms, each of which is a product of two probabilities given above.)
Enter the numerical values for each of the probabilities in the formula for $＿$ to determine is numerical value.
$＿$ $=$
Now you should have all the components to use ＿' theorem to calculate a numerical value for $＿$.
$＿$ $=$
Hide help