How Do You Calculate Conditional Probability?

Let A represent the event "Person has cancer"

Let B represent the event "Person is a smoker"

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We know the probability of the prior event P(A)=0.05 on the basis of past data (5% of patients entering the hospital turn out to have cancer).

The probability of a person being a smoke in the hospital is P(B)=0.45.

P(B|A) (the proportion of smokers among those diagnosed) is 0.75

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Use Bayes rule to compute P(A|B) (The probability of a person having cancer given that they smoke).

*None of this data is accurate