Answer:
There is a 9.6% probability that a person is diagnosed as having cancer.
Step-by-step explanation:
In this problem, we have these following probabilities:
A 5% probability that an adult over 40 has cancer.
This also means that:
There is a 95% probability that an adult over 40 does not have cancer. (Since either the adult has cancer or does not have cancer, and the sum of the probabilities is 100%).
A 78% probability of a person that has cancer being diagnosed,
A 6% probability of a person that does not have cancer being diagnosed.
What is the probability that a person is diagnosed as having cancer?
is the probability of those who have cancer being diagnosed. So it is 78% of 5%. So
is the probability of those who do not have cancer being diagnosed. So it is 6% of 95%. So
So
There is a 9.6% probability that a person is diagnosed as having cancer.