Consider a new (fictional) treatment for lung cancer. When applied to a patient
ID: 3023414 • Letter: C
Question
Consider a new (fictional) treatment for lung cancer. When applied to a patient with lung cancer, the treatment cures the cancer 80% of the time. Unfortunately, there is one well know side-effect, total color blindness, which occurs in 30% of patients who receive the treatment. Additionally, we know that a successful treatment and occurrence of the side-effect happen together in 20% of patients with lung cancer who receive the treatment.
For each of the following, assume the treatment is administered to a randomly selected lung cancer patient.
(a) What is the probability that the treatment does not successfully cure the cancer?
(b) What is the probability that the treatment does not cure the cancer, and the side effect does not occur? Hint: It may be useful to draw a Venn diagram or write out a table.
(c) Given that the treatment successfully cures the cancer, what is the probability that the patient is now color blind?
(d) Are the events {the patient is cured} and {the patient becomes color blind} independent? Why or why not?
Explanation / Answer
Consider a new (fictional) treatment for lung cancer. When applied to a patient with lung cancer, the treatment cures the cancer 80% of the time. Unfortunately, there is one well know side-effect, total color blindness, which occurs in 30% of patients who receive the treatment. Additionally, we know that a successful treatment and occurrence of the side-effect happen together in 20% of patients with lung cancer who receive the treatment.
For each of the following, assume the treatment is administered to a randomly selected lung cancer patient.
Given probabilities
Cured
Not cured
Total
side effect
0.2
0.1
0.3
No side effect
0.6
0.1
0.7
Total
0.8
0.2
1
P=0.20
P=0.10
P=0.6/0.8 =0.75
(d) Are the events {the patient is cured} and {the patient becomes color blind} independent? Why or why not?
A={the patient is cured} and B={the patient becomes color blind}
P( A) =0.8
P(B)=0.3
P( B/A)=0.2/0.8=0.25
P(B) P(B/A)
The events {the patient is cured} and {the patient becomes color blind} are not independent.
Cured
Not cured
Total
side effect
0.2
0.1
0.3
No side effect
0.6
0.1
0.7
Total
0.8
0.2
1
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