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24 October, 17:35

At a certain hospital, 36 patients have lung cancer, 28 patients smoke, and 24 have lung cancer and smoke. Suppose the hospital contains 180 patients. If a patient chosen at random is known to smoke, what is the probability that the patient has lung cancer?

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  1. 24 October, 20:21
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    The probability that a patient chosen at random is known to smoke, also has lung cancer = 2/15 or 13.3%

    Step-by-step explanation:

    1. Let's review the information provided to us to answer this problem correctly:

    Number of patients in the hospital = 180

    Number of patients that have lung cancer = 36

    Number of patients that smoke = 28

    Number of patients that have lung cancer and smoke = 24

    2. If a patient chosen at random is known to smoke, what is the probability that the patient has lung cancer?

    Let's find out the probabilities of the patients mentioned above:

    Probability that a random patient has lung cancer = 36/180 = 1/5

    Probability that a random patient smokes = 28/180 = 7/45

    Probability that a patient chosen at random is known to smoke, also has lung cancer = 24/180 = 4/30 = 2/15 or 13.3%
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