Question 1: Determine which of the following number(s) could represent the probability of an event. (Multiple Answers) a) 0

b) 1.5

c) -1

d) 50%

e) 2/3

Question 2-3: True or False 2. __________ After five tosses of a coin repeatedly producing heads, I believe that this coin is not a fair coin, which means that the probability of head and tail is not half-half. 3. __________ An investment newsletter makes general predictions about the economy to help their clients make sound investment decisions. They advised buying a stock that had gone down in the past four sessions because they said that it was clearly "due to bounce back."

Question 4: Consider rolling a fair six-sided die once with the two possible events, Event A: roll an even number Event B: roll a number less than or equal to 3

State the Sample Space of the whole experiment:

State the Sample Space of the Event A:

State the Sample Space of the Event B:

Draw a Venn diagram in the scratch paper, and find the following probability:

P(A)= P(B)= P (A and B) = P (A or B) =

Question 5: Constructing Contingency Tables: Sometimes we're given probabilities without a contingency table. Although a table isn't always necessary to perform calculations, it is highly suggested that you create one to help keep the information organized.

Example: Facebook reports that there are 70% of their users are from outside the United States, and another report stated that 50% of their users log on to Facebook every day. Facebook also found that 20% of their United States users log on every day.

a) What percentage of Facebook's users are from the United States?

b) What type of probability is the 20% mentioned above?

c) Construct a contingency table showing all the joint and marginal probabilities.

d) What is the probability that a user is from the United States given that he or she logs on every day?

e) Are being from the United States and logging-on every day independent? Explain in detail.

Question 6: Drug Testing of Air Traffic Controllers

ATCs are required to undergo periodic random drug testing. A simple, low-cost urine test is used for initial screening. It has been reported that this particular test has a sensitivity and specificity of 0.96 and 0.93. This means that if there is drug use, the test will detect it 96% of the time. If there is no drug use, the test will be negative 93% of the time. Based on historical results, the FAA reports that the probability of drug use at a given time is approximately 0.007 (this is called the prevalence of drug use).

Draw a probability tree for the situation. (Setup as: Drug Use -> Test Result -> Joint Probabilities), answer the following questions:

a) A positive test result puts the air traffic controller's job in jeopardy. What is the probability of a positive test result?

b) Find the probability an air traffic control truly used drugs, given that the test is positive.

Question 7:

Suppose a supermarket database has 100,000 point-of-sale transactions. Of all these transactions, 2000 include both orange juice and OTC flu medication, and 800 of these also include soup.

a) Find the Support and Confidence for the association rule (OJ and Flu med) (soup)

b) If 1000 of all transactions had soup, find the Lift Ratio for the association rule (OJ and Flu med) (soup)