Assume that the probability of developing lung cancer in smokers is 15%; the probability of developing lung cancer in non-smokers is 1%; and the prevalence of smokers in the U.S. is 20%. If a person is diagnosed with lung cancer, what is the probability that he/she is a smoker?

38%
79%
89%
95%
50%

79%

Thank you Lee!!

To find the probability that a person diagnosed with lung cancer is a smoker, we can use Bayes' theorem. Bayes' theorem allows us to update the probability of an event based on new information.

Let's define the events:
A: The person is a smoker.
B: The person is diagnosed with lung cancer.

We are given the following probabilities:
P(A) = 0.20 (the prevalence of smokers in the U.S.)
P(B|A) = 0.15 (the probability of developing lung cancer in smokers)
P(B|A') = 0.01 (the probability of developing lung cancer in non-smokers)

We want to find P(A|B), the probability that the person is a smoker given that they are diagnosed with lung cancer.

Using Bayes' theorem:
P(A|B) = (P(A) * P(B|A)) / (P(A) * P(B|A) + P(A') * P(B|A'))

Let's substitute the values:
P(A|B) = (0.20 * 0.15) / (0.20 * 0.15 + (1 - 0.20) * 0.01)
= 0.03 / (0.03 + 0.80 * 0.01)
= 0.03 / (0.03 + 0.008)
= 0.03 / 0.038
≈ 0.7895

Therefore, the probability that a person diagnosed with lung cancer is a smoker is approximately 0.7895, which is approximately 79%. So, the correct answer is 79%.