Researchers have long been interested in the relationship between cigarette smoking and lung cancer. Suppose that...
Researchers have long been interested in the relationship between cigarette smoking and lung cancer. Suppose that in a recent survey of adult males, the following relative frequencies were observed:
Smokes = 0.25 Gets cancer = 0.11 Smokes AND gets cancer = 0.08
If one adult female is randomly selected, find the probability that she: (A venn diagram will help)
i. Smokes or gets cancer _________
ii. Does Not smoke OR does not get cancer __________
iii. Gets cancer given that she smokes ___________
iv. Gets cancer knowing she does not smoke ____________
Homework Answers
We are given here that:
P(smokes) = 0.25,
P( gets cancer) = 0.11
P( smokes and gets cancer) = 0.08
a) Using law of probability, we have here:
P( smokes or gets cancer) = P(smokes) + P(gets cancer) - P(smokes
and gets cancer)
P( smokes or gets cancer) = 0.25 + 0.11 - 0.08 = 0.28
Therefore 0.28 is the required probability here.
b) P(does not smoke or does not cancer)
= 1 - P(smokes and gets cancer)
= 1 - 0.08
= 0.92
Therefore 0.92 is the required probability here.
c) Given that she smokes, probability that she gets cancer is
computed using bayes theorem here as:
P( gets cancer | smokes) = P(smokes and gets cancer) / P(smokes) =
0.08 / 0.25 = 0.32
Therefore 0.32 is the required probability here.
d) P(gets cancer knowing that she does not smoke)
= [ P(gets cancer) - P(gets cancer and smokes) ] /P(does not
smoke)
= (0.11 - 0.08) / (1 - 0.25)
= 0.04
therefore 0.04 is the required probability here.
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