The results of a study that tried to determine the effects of smoking on lung ca
ID: 3174340 • Letter: T
Question
The results of a study that tried to determine the effects of smoking on lung cancer in a study group was as follows:
Has lung cancer
No lung cancer
Smoker
9
3
Non-Smoker
6
57
a. Are the events “Non-smoker” and “No lung cancer” independent?
b. The study was later modified and one more group of individuals were included:
Has lung cancer
No lung cancer
Smoker
0.08
0.01
Non-Smoker
0.06
0.79
Quit smoking
If events “Quit smoking” and “No lung cancer” are mutually exclusive, what is the probability that a person has quit smoking and has lung cancer?
Has lung cancer
No lung cancer
Smoker
9
3
Non-Smoker
6
57
Explanation / Answer
a)
P(non smoker) = 63/75
P(No lung cancer) = 60/75
P(non smoker and No lung cancer) = 57/75
Since P(non smoker and No lung cancer) P(non smoker) * P(No lung cancer), the events “Non-smoker” and “No lung cancer” are not independent.
b. If events “Quit smoking” and “No lung cancer” are mutually exclusive, then P(Quit smoking and No lung cancer) = 0. Sum of all probabilities in the table must be 1. Therefore, complete table is:
Has lung cancer
No lung cancer
Smoker
0.08
0.01
Non-Smoker
0.06
0.79
Quit smoking
1-(0.08+0.01+0.06+0.79) = 0.06
0
Has lung cancer No lung cancer Total Smoker 9 3 12 Non-Smoker 6 57 63 Total 15 60 75Related Questions
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