## Probability Homework

Solve these problems, then check your answers against the given solutions.

### Exercises

##### Exercise 1

Suppose that you have 8 cards. 5 are green and 3 are yellow. The 5 green cards are numbered 1, 2, 3, 4, and 5. The 3 yellow cards are numbered 1, 2, and 3. The cards are well shuffled. You randomly draw one card.

- G = card drawn is green
- E = card drawn is even-numbered

- List the sample space.
- P(G) =
- P(G\E) =
- P(G AND E) =
- P(G OR E) =
- Are G and E mutually exclusive? Justify your answer numerically.

##### Exercise 2

An experiment consists of tossing a nickel, a dime and a quarter. Of interest is the side the coin lands on. - List the sample space.
- Let A be the event that there are at least two tails. Find P(A).
- Let B be the event that the first and second tosses land on heads. Are the events A and B mutually exclusive? Explain your answer in 1 - 3 complete sentences, including justification.

##### 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: - P(U AND V) =
- P(U I V) =
- P(U OR V) =

##### Exercise 5

The following table identifies a group of children by one of four hair colors, and by type of hair.

Hair Type |
Brown | Blond | Black | Red | Totals |
---|---|---|---|---|---|

Wavy | 20 | 15 | 3 | 43 | |

Straight | 80 | 15 | 12 | ||

Totals | 20 | 215 |

Table 3.2

- Complete the table above.
- What is the probability that a randomly selected child will have wavy hair?
- What is the probability that a randomly selected child will have either brown or blond hair?
- What is the probability that a randomly selected child will have wavy brown hair?
- What is the probability that a randomly selected child will have red hair, given that he has straight hair?
- If B is the event of a child having brown hair, find the probability of the complement of B.
- 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

Finish each probability statement by matching the correct answer.

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 |

Table 3.4

##### Exercise 7

Given events G and H: P(G) = 0.43 ; P(H) = 0.26 ; P(H and G) = 0.14- Find P(H or G)
- Find the probability of the complement of event (H and G)
- 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.- Find the probability that a person has both type O blood and the Rh- factor
- 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. - Find the probability that a course has a final exam or a research project.
- 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- Find P(D and E)
- Find P(E I D)
- Find P(D or E)
- Using an appropriate test, show whether D and E are independent.
- Using an appropriate test, show whether D and E are mutually exclusive.

Source: Barbara Illowsky and Susan Dean, https://archive.org/details/CollaborativeStatisticsHomeworkBook/page/n48/mode/1up

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