Brain tumors in children are rare:the base rate is only about 1/10,000.A child with a tumor is very likely to have occasional headaches:99 out of 100do.But there are many other reasons a child can have a headache: of those who do not have a tumor,1 in 10have occasional headaches.

1. Given that a child has occasional headaches (H), what it the probability that he or she has a brain tumor (T)?Show your work.

2.Name a behavioral bias that may occur when estimating the probability that your child has a brain tumor. Would this bias lead to under-or-overestimate that probability? Explain.

3. Among children with headaches (H), 999/1000 will ultimately be fine (F). Suppose that a physician using a simple test can correctly determine whether the child is fine or not in 95/100 of children with headaches. Given that the doctor after performing the test gives the patient a green light (G), what is the probability that the childreally will be fine?Show your work.