Question One: $1418$ men were cross$-$classified according to their

smoking status and their lung cancer status as in the following

table:

If one of these men is selected at random, find the probability

that he is $.$

a$)$ non$-$smoker or having lung cancer.

b$)$ having lung cancer, given that he is a smoker.

c$)$ a smoker, given that he does not have lung cancer.

d$)$ Are the events "being a smoker "and "having lung cancer

"independent? Why?

Question Two:

A lab test is $95$ percent effective at detecting a certain disease

when it is present. When the disease is not present, the test is $99$

percent effective at declaring the subject negative. If $8$ percent of

the population has the disease, what is the probability that a

subject has the disease given that his test is positive?