At a certain hospital, 40 patients have lung cancer, 30 patients smoke, and 25 have
lung cancer and smoke. Suppose the hospital has 200 patients. If a patient chosen at
random is known to smoke, what is the probability that the patient has lung cancer?
25/200
To calculate the probability that a patient chosen at random who smokes has lung cancer, we can use conditional probability.
Conditional probability is the likelihood of an event occurring given that another event has already occurred. In this case, we want to find the probability that a patient has lung cancer, given that they smoke.
We are given the following information:
- Number of patients with lung cancer (A) = 40
- Number of patients who smoke (B) = 30
- Number of patients with lung cancer and who smoke (A ∩ B) = 25
- Total number of patients (N) = 200
To find the probability, we can use the formula for conditional probability:
P(A|B) = P(A ∩ B) / P(B)
Where P(A ∩ B) denotes the probability of both events A and B happening together, and P(B) denotes the probability of event B occurring.
In our case, we know that P(A ∩ B) = 25 and P(B) = 30. So, we can substitute these values into the formula:
P(A|B) = 25 / 30
Therefore, the probability that a patient chosen at random who smokes has lung cancer is 25/30, or approximately 0.83.