Question

1. Walgreens sells both Kleenex and NyQuil. In a random sample of 5000 purchases, it was found that 1200 contained Kleenex and 540 contained NyQuil. These are not independent because sick people are more likely to buy both and healthy people more likely to buy neither. In looking into that, it was found that 360 purchases contained both.

a. Make a two-way table to display this information. Fill in the table with the missing entries, and be sure your table has row and column totals.

b. If we randomly select a purchase that contained Kleenex, what is the probability it also contained NyQuil?

c. What percent of all purchases didn’t contain either product?

2. The probability that a U.S. resident has traveled to Canada is 0.18 and to Mexico is 0.09.

a. If traveling to Canada and traveling to Mexico are independent events, what is the probability that a randomly-selected person has traveled to both? (page 109 in the book may help)

b. It turns out that only 4% of U.S. residents have traveled to both countries. Comparing this with your answer to part a, are the events independent? Explain why or why not. (page 119 may help)

c. Using the %’s given, make a Venn Diagram to display this information. (Don’t use your answer to part a.)

d. Using the conditional probability formula (page 114 in the book) and the %’s given, find the probability that a randomly-selected person has traveled to Canada, if we know they have traveled to Mexico.

Answer 1

a)

		Kleenex
		yes	no
Nyquil	yes	360	180	540
	no	840	3620	4460
		1200	3800	5000

		Kleenex
		yes	no
Nyquil	yes	360	=E3-C3	540
	no	=C5-C3	=D5-D3	=E5-E3
		1200	=E5-C5	5000

b)
P(Nyquil| Kleenex)
= P(Nyquil and Kleenex| Kleenex)
= 360/1200
=0.3

c)
3620/5000
= 0.724