PRINTABLE VERSION Quiz 10

Transcription

1 1 of 8 4/9/2013 8:17 AM PRINTABLE VERSION Quiz 10 Question 1 Let A and B be events in a sample space S such that P(A) = 0.34, P(B) = 0.39 and P(A B) = Find P(A B). a) b) c) d) e) Question 2 Let A and B be events in a sample space S such that P(A) = , P(B) = , and P(A B) = Find P(B A c ). Hint: Draw a Venn Diagram to find P(A c B). a) b) c) d) e) Question 3 Suppose that A and B are independent events. If P(A) = 1 5 and P(B) = 7 10, find P(A B). a) 0.02

2 b) 1.00 c) 0.07 d) 0.09 e) 0.14 Question 4 Quality 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) = 7 50 P(B) = 4 25 P(C) = 3 20 P(D) = Assuming independence, what is the probability on a particular day that all machines will break down? a) b) c) d) e) Question 5 A pair of fair dice is cast. What is the probabiliy that one of the numbers falling uppermost is a 5, given that the two numbers falling uppermost are different? a) b) c) d) of 8 4/9/2013 8:17 AM

3 3 of 8 4/9/2013 8:17 AM e) 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 a Diamond and the second card drawn is not a Diamond? a) b) c) d) e) Question 7 Suppose we have two urns, Urn 1 and Urn 2. Urn 1 contains 3 red marbles and 5 white marbles. Urn 2 contains 9 red marbles and 11 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) b) c) d) e) 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 7% of the compact disks produced by manufacturer I are defective, 5% of those produced by manufacturer II are defective, and 4% of those produced by manufacturer III are defective. Manufacturers I, II, and III supply 37%, 45%, and 18%, 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?

4 4 of 8 4/9/2013 8:17 AM a) b) c) d) e) Question 9 Suppose that 8 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) b) c) d) e) Question 10 Suppose that 6 green balls and 9 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) b) c) d) e) Question 11

5 5 of 8 4/9/2013 8:17 AM 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, 17% 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) b) c) d) e) 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 98% 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) b) c) d) e) Question 13 Urn A contains 12 yellow balls and 4 red balls. Urn B contains 6 yellow balls and 9 red balls. Urn C contains 10 yellow balls and 3 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) b)

6 6 of 8 4/9/2013 8:17 AM c) d) e) Question yellow balls and 14 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) b) c) d) e) 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) b) c) d) e) Question 16 King Mattress purchases Sleep-n-Air mattresses from three different distributors. The probability of

7 7 of 8 4/9/2013 8:17 AM getting a defective mattress from Distributor A, B, or C is 0.18, 0.12, and 0.54, 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 A? a) b) c) d) e) Question 17 There are three colored cookie jars. One jar is blue, another green and the last one pink. The blue jar contains 10 chocolate chip and 7 sugar cookies. The green jar contains 8 chocolate chip, 14 sugar and 11 peanut butter cookies. The pink jar contains 6 chocolate chip, 5 sugar and 9 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 1 2, 1 4, and 1 4, 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) b) c) d) e) 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 15 brown marbles and 14 clear marbles. Urn 2 contains 6 brown marbles, 11 clear marbles and 9 red marbles. Urn 3 contains 7 brown marbles, 8 clear marbles and 5 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)

8 8 of 8 4/9/2013 8:17 AM b) c) d) e)