3. Here are the probabilities of developing lung cancer for patients based on th
ID: 3124323 • Letter: 3
Question
3. Here are the probabilities of developing lung cancer for patients based on their history of employment as a miner (yes/no) and their smoking behavior (None, < 1 pack, 1 pack or more)
Smoking Behavior
Non-smoker
Smoker of <1 pack
Smoker of 1 pack or more
Lung Cancer
Yes
.04
.08
.23
No
.60
.10
.05
What is the probability that the patient has lung cancer?
What is the probability the patient is a non-smoker?
What is the probability the patient is smoker of > 1 pack and has lung cancer?
Smoking Behavior
Non-smoker
Smoker of <1 pack
Smoker of 1 pack or more
Lung Cancer
Yes
.04
.08
.23
No
.60
.10
.05
Explanation / Answer
What is the probability that the patient has lung cancer?
P(C) = 0.04 + 0.08 + 0.23 = 0.35 [ANSWER]
*******************
What is the probability the patient is a non-smoker?
P(NS) = 0.04 + 0.60 = 0.64 [ANSWER]
*****************
P(C|S>1) = 0.23/(0.23+0.05) = 0.821428571 [ANSWER]
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