The probability that a man develops some form of cancer in his lifetime is $0.4567.$The probability that a man has at least one false positive test result (meaning the test comes back for cancer when the man does not have it) is $0.51.$

Let: C = a man develops cancer in his lifetime; P = man has at least one false positive. Construct a tree diagram of the situation.

The probability that a man develops some form of cancer in his lifetime is $0.4567$. The probability that a man has at least one false positive test result (meaning the test comes back for cancer when the man does not have it) is $0.51.$

Here, in this question we have given that the probability that a man develops cancer in his whole life is $0.4567$and will not develop is $0.5433.$

Now Probability person who develops cancer in his lifetime can have false positive report is zero because if a person develops cancer then report can't show falsely positive because result is already positive and now Probability person who develops cancer in his lifetime can have false negative is $0$because he is already have develops cancer then it's for sure that if report show negative then its probability of being false is $1.$

Now, about the man who does not develops cancer, the probability of getting false positive report is $0.51$and the probability of getting false negative is $0.49.$

The tree diagram is

The tree diagram is :