1.Suppose that a certain HIV test has both a sensitivity and specificity of 99.9%. This test is applied to a population of 1,000,000 people.

Suppose that the population comes from the blood donor pool that has already been screened. In this population,0.3% of the population is actually infected with HIV.

(a) Calculate the PPV.Suggestion: First make a table as seen below. (Round your answer to one decimal place.)

%

Has disease Does not have disease Totals

Test positive

Test negative

Totals

(b) Calculate the NPV. (Round your answer to four decimal places.)

%

(c) How many people will test positive who are, in fact, disease-free?

2The total area of the United States is 3.79 million square miles, andNew Mexicocovers0.12million square miles. A meteor falls from the sky and strikes Earth. What is the probability that it strikesNew Mexicogiven that it strikes the United States? (Round your answer to one decimal place.)

3.How many possible outcomes are there if we toss10dice, each of a different color?

N= possible outcomes

4.Suppose an opaque jar contains3red marbles and 10 green marbles. The following exercise refers to the experiment of picking two marbles from the jar without replacing the first one.

What is the probability of getting a green marble and a red marble? (Enter your probability as a fraction.Hint:How is this exercise different from finding the probability of getting a green marble first and a red marble second?)

The following exercise refers to choosing two cards from a thoroughly shuffled deck. Assume that the deck is shuffled after a card is returned to the deck.

If you do not put the first card back in the deck before you draw the next, what is the probability that the first card is aheartand the second card is aspade? (Enter your probability as a fraction.)