Lecture 11- Probability Trees 2 Flashcards
Sam, Lee and Kai decide to play a game of chicken. There are six
similar bikes, two of which have had the brakes disabled. Each person
chooses a bike at random, cycles at high speed towards a river
swimming hole, and brakes in time to stop. The game ends when the
first person cycles into the river. They decide to proceed in reverse
alphabetical order.
Find Pr(each will lose) and Pr(no loser)
Pr (Sam loses)= 5/15
Pr (Lee loses)= 4/15
Pr (Kai loses)= 3/15
Pr (no loser)= 3/15
working on slides/ in lecture 11 notes. This is an example of dependent probabilities
What are diagnostic tests used for?
To determine whether or not a person has a particular disease
What is sensitivity in terms of diagnostic tests?
SENSITIVITY = Pr(B | A)
Think of this as “the probability of a positive test result, given the
person actually has the disease.
What is specificity in terms of diagnostic tests?
SPECIFICITY = Pr(B¯ | A¯)
Think of this as “the probability of a negative test result, given the
person does NOT have the disease.
What is positive predictive value?
POSITIVE PREDICTIVE VALUE = Pr(A | B)
The proportion of patients with positive test results who are correctly
diagnosed.
What is negative predictive value?
NEGATIVE PREDICTIVE VALUE = Pr(A¯ | B¯)
The proportion of patients with negative test results who are correctly
diagnosed.
How do you designate the variables for talking about sensitivity and specificity?
A: some condition (A) is present.
B: the related test (B) for the presence of A is positive.
Note: This test result may or may not be correct.
A patient with haematuria (blood in the urine) presents to a urologist
for investigation. A possible diagnosis is bladder cancer. The
CxBladder test was developed to detect bladder cancer cells in the
urine.
Suppose there is a probability of 0.612 that a person with bladder
cancer will have a positive CxBladder test, and a probability of 0.849
that a person without bladder cancer will have a negative test.
In this population of people presenting to a urologist with haematuria,
the prevalence of bladder cancer is 13.8%
Find the probability that a person with a positive CxBladder test had
bladder cancer.
0.394
See answers in lecture slides + working
A patient with haematuria (blood in the urine) presents to a urologist
for investigation. A possible diagnosis is bladder cancer. The
CxBladder test was developed to detect bladder cancer cells in the
urine.
Suppose there is a probability of 0.612 that a person with bladder
cancer will have a positive CxBladder test, and a probability of 0.849
that a person without bladder cancer will have a negative test.
In this population of people presenting to a urologist with haematuria,
the prevalence of bladder cancer is 13.8%
Find the probability that a person with a positive CxBladder test had
bladder cancer.
Find the positive predictive value
0.394 (check slides)
A patient with haematuria (blood in the urine) presents to a urologist
for investigation. A possible diagnosis is bladder cancer. The
CxBladder test was developed to detect bladder cancer cells in the
urine.
Suppose there is a probability of 0.612 that a person with bladder
cancer will have a positive CxBladder test, and a probability of 0.849
that a person without bladder cancer will have a negative test.
In this population of people presenting to a urologist with haematuria,
the prevalence of bladder cancer is 13.8%
Find the probability that a person with a positive CxBladder test had
bladder cancer.
Find the negative predictive value…
0.932
Pr(B) =
Pr(B ∩ A) + Pr(B ∩ A¯)
Pr(B¯)=
= Pr(B¯ ∩ A) + Pr(B¯ ∩ A¯)
Pr(A|B)=
Pr(A ∩ B)/ Pr(B)
which is Positive Predictive Value
Pr(A¯|B¯)=
Pr(A¯∩ B¯)/ Pr(B¯)
which is Negative Predictive Value
