The probability an adult male in the U.S. will be diagnosed with lung cancer in
ID: 3206872 • Letter: T
Question
The probability an adult male in the U.S. will be diagnosed with lung cancer in his lifetime is 0.071. About 16.7% of men 18 and over in the U.S. smoke and the probability a male who smokes will be diagnosed with lung cancer is 0.31.
a. Find the probability a randomly selected adult male in the U.S. will be a non-smoker. b. Find the probability a randomly selected adult male in the U.S. will be a smoker and be diagnosed with lung cancer.
c. Find the probability a randomly selected adult male in the U.S. will be a non-smoker and be diagnosed with lung cancer.
d. Find the probability a randomly selected adult male in the U.S. will be a smoker or be diagnosed with lung cancer.
e. Find the probability a randomly selected adult male in the U.S. be diagnosed with lung cancer if he’s a non-smoker.
f. Are smoking status and diagnosis with lung cancer independent? Justify your answer with probabilities.
g. Find the probability a randomly selected adult male in the U.S. who has been diagnosed with lung cancer is a smoker.
Explanation / Answer
Let event an adult male in the U.S. will be diagnosed with lung cancer be L and event men 18 and over in the U.S. smoke be S. Given:
P(L) = 0.071
P(S) = 0.167
P(L|S) = 0.31
a. P(S') = 1 - 0.167 = 0.833
b. P(L and S) = P(L|S) P(S) = 0.31 * 0.167 = 0.05177
c. P(L and S') = P(L|S') P(S') = (0.071-0.31) * 0.833 = 0.199087
d. P(L or S) = P(L) + P(S) - P(L and S) = 0.071 + 0.167 - 0.05177 = 0.18623
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