The probability an adult male in the U.S. will be diagnosed with lung cancer in

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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