1. See the 2 by 2 table. Say the context is that on a Saturday a store has 85 customers who ask a sales rep about a particular product. In the table you see a breakdown of those who had not seen an advertisement for the product and those who had and those who did not or did make a purchase.

Had not seen ad Y1 Saw ad Y2
Did not purchase X1 4 13
Made purchase X2 16 52

P(X2 Y1) =
P(X1 or Y2) =
P(X1 given Y2) =

While it seems that seeing the ad generated a great deal of traffic, is the notion of making a purchase independent or dependent on the idea of seeing the ad? Explain your answer.

2. All bags entering a research facility are screened. Ninety-seven percent of the bags that contain forbidden material trigger an alarm. Fifteen percent of the bags that do not contain forbidden material also trigger the alarm. If 1 out of every 1,000 bags entering the building contains forbidden material, what is the probability that a bag that triggers the alarm will actually contain forbidden material?
a. 0.00097
b. 0.00640
c. 0.03000
d. 0.14550
e. 0.97000