BUS204: Business Statistics

Exercise 3

E and F mutually exclusive events. P (E) = 0.4; P (F) = 0.5. Find P (E \ F).

Exercise 4

U and V are mutually exclusive events. P (17) = 0.26; P (V) = 0.37. Find:

1. P(U AND V) =
2. P(U I V) =
3. P(U OR V) =

Exercise 5

Hair Type	Brown	Blond	Black	Red	Totals
Wavy	20		15	3	43
Straight	80	15		12
Totals		20			215

1. Complete the table above.
2. What is the probability that a randomly selected child will have wavy hair?
3. What is the probability that a randomly selected child will have either brown or blond hair?
4. What is the probability that a randomly selected child will have wavy brown hair?
5. What is the probability that a randomly selected child will have red hair, given that he has straight hair?
6. If B is the event of a child having brown hair, find the probability of the complement of B.
7. In words, what does the complement of B represent?

Exercise 6

Approximately 249,000,000 people live in the United States. Of these people, 31,800,000 speak a language other than English at home. Of those who speak another language at home, over 50 percent speak Spanish. (Source: U.S. Bureau of the Census, 1990 Census)

Let: E = speak English at home; E' = speak another language at home; S = speak Spanish at home

Probability Statements	Answers
a. P(E') =	i. 0.8723
b. P(E) =	ii. > 0.50
c. P(S) =	iii. 0.1277
d. P(S 1 E') =	iv. > 0.0639

Exercise 7

Given events G and H: P(G) = 0.43 ; P(H) = 0.26 ; P(H and G) = 0.14

1. Find P(H or G)
2. Find the probability of the complement of event (H and G)
3. Find the probability of the complement of event (H or G)

Exercise 8

United Blood Services is a blood bank that serves more than 500 hospitals in 18 states. According to their website, http://www.unitedbloodservices.org/humanbloodtypes.html, a person with type O blood and a negative Rh factor (Rh- ) can donate blood to any person with any blood type. Their data show that 43% of people have type O blood and 15% of people have Rh- factor; 52% of people have type O or Rh— factor.

1. Find the probability that a person has both type O blood and the Rh- factor
2. Find the probability that a person does NOT have both type O blood and the Rh- factor.

Exercise 9

At a college, 72% of courses have final exams and 46% of courses require research papers. Suppose that 32% of courses have a research paper and a final exam. Let F be the event that a course has a final exam. Let R be the event that a course requires a research paper.

1. Find the probability that a course has a final exam or a research project.
2. Find the probability that a course has NEITHER of these two requirements.

Exercise 10

A college finds that 10% of students have taken a distance learning class and that 40% of students are part time students. Of the part time students, 20% have taken a distance learning class. Let D = event that a student takes a distance learning class and E = event that a student is a part time student

1. Find P(D and E)
2. Find P(E I D)
3. Find P(D or E)
4. Using an appropriate test, show whether D and E are independent.
5. Using an appropriate test, show whether D and E are mutually exclusive.