phi 2130 argument inferences probability questions due march 25 2020 1 hour

PHI-2130 Argument & Inferences Probability Questions need in 1 hour

. Instructions

1. Instructions The rules you need to solve the problems are as follows:
2. General Conjunction Rule, used only for dependent (associated) variables: P(A & B) = P(A) x P(B/A)
3. Special Conjunction Rule, used only for independent (nonassociated) variables. P(A & B) = P(A) x P(B)
4. General Disjunction Rule, used only for nonexclusive values. P(A or B) = [P(A) + P(B)] – P(A & B)
5. Special Disjunction Rule, used only for inclusive values. P(A or B) = P(A) + P(B)
6. Conditional Probability Rule P(B/A) = P(A & B) divided by P(A) Relative Risk RR(y1 when x1) = P(y1 given x1) divided by P(y1 given x2)

1. A jar of marbles contains the following:

45 red marbles. Of these, 25 are large; 20 are small.

39 green marbles. Of these, 16 are large; 23 are small.

32 blue marbles. Of these, 25 are large; 7 are small.

24 yellow marbles. Of these, 9 are large and 15 are small.

Calculate the following. Show your work. (6 points per question, for a total of 42 points):

(a) If a marble is taken from this population, what is the probability that it will be yellow or green?

(b) If a marble is taken from this population, what is the probability that it will be blue or yellow?

(c) Construct a diagram of this population, using the values “red” and “nonred” for color. You do not have to turn in the diagram; use it to answer the rest of the questions. This is 6 free points since I won’t be grading your diagram. It is only to help you.

(d) If a marble is selected from this population, what is the probability that it will be red and large?

(e) If a marble is selected from this population, what is the probability that it will be red or large?

(f) If a marble is selected from this population, what is the probability that it will be red and small?

(g) If a marble is selected from this population, what is the probability that it will be red or small.

. A jar contains 68% orange marbles. Calculate the following. Show your work. (7 points per question, for a total of 28 points).

(a) If three marbles are selected from the jar, what is the probability that all of them will be orange?

(b) If three marbles are selected from the jar, what is the probability that exactly two will be orange?

(c) If three marbles are selected from the jar, what is the probability that one (and only one) will be orange?

(d) If three marbles are selected from the jar, what is the probably that zero will be red?

Question 3

Relative risk problems (5 points per question, for a total of 30 points). Show your work.

A, On a piece of scrap paper, draw a diagram using the following data, putting “vaccinated” and “nonvaccinated at the top and on the sides put “Disease A present” and “Disease A absent”.You do not have to make a diagram if you can answer the question without it, and the diagram itself will not be graded.

15% have Disease A if vaccinated and 85% do not. have disease A.

30% have Disease A if not vaccinated, and 70% do not have the disease.

Now answer the following two questions:

(a) What is the relative risk of having the disease when not vaccinated vs. the risk of having it when vaccinated?

(b) What is the relative risk of having the disease when vaccinated vs. having it when not vaccinated?

B. Same directions, but on this diagram put “Lung Cancer Present” and “Lung Cancer Absent” at the top and “Smoker” and “Nonsmoker” on the side. 12% of smokers get lung cancer; 88% do not. 1.2% of nonsmokers get lung cancer and 98.8% do not *(this is the actual data). Answer the following two questions:

(a) What is the relative risk of a smoker getting lung cancer vs. a nonsmoker?

(b) What is the relative risk lof a nonsmoker getting lung cancer vs. a smoker?

C. Same directions, but on the top put “Study two hours” and “Do not study”; on the side put “pass the test” and “fail the test.” Of those who study two hours, 84% passed the test. Of those who did not study, 42% passed the test. Answer the following two questions:

(a) What is the relative risk of failing the test when not studying two hours vs. failing the test and studying two hours?

(b) What is the relative risk of failing the test when studying two hours vs. the risk of failing and not studying?

EXTRA CREDIT (up to ten points): In a box of chess pieces, half the pieces are black and half are white. In total, there are 32 chess pieces. There are two kings, a black king and a white queen. There are 16 pawns, of which 50% are black and 50% are white. The probability of randomly selecting a black pawn from the box is 8/32 or .25. A pawn is selected from the box. What is the probability that it is black. That is, what is the probability of pawn/black. Using the conditional probability rule, solve this problem.