Question 1 Let A and B be events in a sample space S such that P(A) = 0.37, P(B) = 0.49 and P(A B) = 0.11. Find P(A | B).

a)0.7551

b)0.1279

c)0.0204

d)0.2973

e)0.2245

f)None of the above.

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Question 2 Let A and B be events in a sample space S such that P(A) =⁷₂₅, P(B) =¹₂, and P(A B) =¹₂₀. Find P(B | A^c).

Hint: Draw a Venn Diagram to find P(A^c B).

a)0.6250

b)1.7857

c)0.6944

d)0.9000

e)0.0694

f)None of the above.

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Question 3 Suppose that A and B are independent events. If P(A) =³₁₀ and P(B) =¹₂, find P(A B).

a)0.15

b)0.03

c)1.00

d)0.08

e)0.05

f)None of the above.

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Question 4Quality Control:A company has four photocopy machines A, B, C and D. The probability that a given machine will break down on a particular day is

P(A) =¹₅P(B) =³₂₅P(C) =³₂₅P(D) =⁷₅₀

Assuming independence, what is the probability on a particular day that all machines will break down?

a)0.24801587

b)0.00000240

c)0.01000000

d)0.00040320

e)0.00248016

f)None of the above.

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Question 5 A pair of fair dice is cast. What is the probabiliy that at least one of the numbers falling uppermost is a 1, given that the sum of the numbers falling uppermost is even?

a)0.3667

b)0.4545

c)0.3056

d)0.2778

e)0.1389

f)None of the above.

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Question 6 Two cards are drawn without replacement from a well-shuffled deck of 52 playing cards. What is the probability that the first card drawn is a5 and the second card drawn is a6?

a)0.0060

b)0.0059

c)0.0045

d)0.1569

e)0.1554

f)None of the above.

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Question 7 Suppose we have two urns, Urn 1 and Urn 2. Urn 1 contains 9 red marbles and 3 white marbles. Urn 2 contains 11 red marbles and 5 white marbles. The experiment consists of first choosing an urn with equally likely probability, and then drawing a marble from that urn. What is the probability of choosing Urn 2 and a red marble?

a)0.3750

b)0.3125

c)0.1250

d)0.7500

e)0.3438

f)None of the above.

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Question 8 A recording company obtains the blank CDs used to produce its labels from three compact disk manufacturers: I, II, and III. The quality control department of the company has determined that 3% of the compact disks produced by manufacturer I are defective, 5% of those produced by manufacturer II are defective, and 5% of those produced by manufacturer III are defective. Manufacturers I, II, and III supply 36%, 54%, and 10%, respectively, of the compact disks used by the company. What is the probability that a randomly selected label produced by the company will contain a defective compact disk?

a)0.0050

b)0.1300

c)0.0270

d)0.0428

e)0.0108

f)None of the above.

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Question 9 Suppose that 10 green balls and 14 purple balls are placed in an urn. Two balls are then drawn in succession. What is the probability that the second ball drawn is a purple ball if the first ball is replaced before the second is drawn?

a)0.1224

b)0.6250

c)0.8333

d)0.4167

e)0.5833

f)None of the above.

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Question 10 Suppose that 11 green balls and 14 purple balls are placed in an urn. Two balls are then drawn in succession. What is the probability that both balls drawn have the same color if the first ball is replaced before the second is drawn?

a)0.3136

b)0.0448

c)0.5072

d)0.2464

e)0.1936

f)None of the above.

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Question 11 Seniors at a certain high school took a survey regarding future plans. All plan to attend college some time; however, 76% plan to go to college immediately following high school. Of those who plan to attend college immediately following high school, 18% plan to major in Math. Of those who do not plan to attend college immediately following high school, 11% plan to major in Math. What is the probability that a randomly chosen senior does not plan to attend college immediately following high school and plans to major in Math.

a)0.1100

b)0.1800

c)0.8900

d)0.1368

e)0.0264

f)None of the above.

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Question 12 A new test to detect TB has been designed. It is estimated that 87% of people taking this test have the disease. The test detects the disease in 97% of those who have the disease. The test does not detect the disease in 99% of those who do not have the disease. If a person taking the test is chosen at random, what is the probability of the test indicating that the person does not have the disease?

a)0.0261

b)0.0100

c)0.1548

d)0.0300

e)0.9900

f)None of the above.

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Question 13 Urn A contains 9 yellow balls and 6 red balls. Urn B contains 5 yellow balls and 12 red balls. Urn C contains 11 yellow balls and 12 red balls. An urn is picked randomly (assume that each urn is equally likely to be chosen), and then a ball is picked from the selected urn. What is the probability that the chosen ball came from urn B, given that it was a yellow ball?

a)0.0528

b)0.3485

c)0.0549

d)0.4372

e)0.2143

f)None of the above.

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Question 14 14 yellow balls and 6 red balls are placed in an urn. Two balls are then drawn in succession without replacement. What is the probability that the first ball drawn is a red ball if the second ball drawn is yellow?

a)0.7000

b)0.6786

c)0.3500

d)0.5556

e)0.3158

f)None of the above.

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Question 15 An arcade booth at a county fair has a person pick a coin from two possible coins available and then toss it. If the coin chosen lands on heads, the person gets a prize. One coin is a fair coin and one coin is a biased coin (unfair) with only a 37% chance of getting a head. Assuming equally likely probability of picking either coin, what is the probability that the fair coin is the one chosen, given that the chosen coin lands on heads?

a)0.4032

b)0.5747

c)0.0133

d)0.8700

e)0.4350

f)None of the above.

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Question 16 King Mattress purchases Sleep-n-Air mattresses from three different distributors. The probability of getting a defective mattress from Distributor A, B, or C is 0.15, 0.68, and 0.13, respectively. Assume an equal probability of making a purchase from each distributor A, B, or C. If King Mattress sells a defective mattress, what is the probability that it came from Distributor B?

a)0.1354

b)0.7083

c)0.2000

d)0.0441

e)0.1563

f)None of the above.

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Question 17 There are three colored cookie jars. One jar is blue, another green and the last one pink. The blue jar contains 14 chocolate chip and 11 sugar cookies. The green jar contains 6 chocolate chip, 9 sugar and 10 peanut butter cookies. The pink jar contains 13 chocolate chip, 15 sugar and 5 peanut butter cookies. One of the three cookie jars is chosen at random. The probabilities that the blue jar, green jar, or pink jar will be chosen are ¹₂, ¹₄, and ¹₄, respectively. A cookie is then chosen at random from the chosen jar. What is the probability that the pink jar was chosen, if it is known that the cookie was a sugar cookie?

a)0.2682

b)0.1136

c)0.3623

d)0.4545

e)0.1515

f)None of the above.

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Question 18 An experiment consists of choosing an urn with the following probabilities that Urn 1, Urn 2, or Urn 3 will be chosen: 1/2, 1/4, and 1/4, respectively. Urn 1 contains 14 brown marbles and 13 clear marbles. Urn 2 contains 15 brown marbles, 5 clear marbles and 10 red marbles. Urn 3 contains 12 brown marbles, 11 clear marbles and 7 red marbles.

A marble is then chosen from the chosen urn. What is the probability that Urn 3 was chosen, given that the marble chosen was clear?

a)0.0917

b)0.2450

c)0.1222

d)0.3613

e)0.3667

f)None of the above.

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