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Question1:

Suppose there are two boxes, the 1st one contains three green and one red balls, whereas the second contains two green and two red balls. First, a box is chosen at random and then a ball is drawn randomly from that box.

a) What is the probability that the ball drawn is green?

b) If the ball drawn was green, what is the probability that the 1st box was chosen?

Question 2:

Consider a high-risk population where 10% of the people have HIV. A diagnostic test is correct in 90% of the cases if the person has, and in 95% of the cases if the person does not have the virus. If a person is tested positive, what is the probability that the person does not have HIV?

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