Exam 12: Counting and Probability

Solve the problem. -The following data represent the marital status of females 18 years and older in a certain U.S. city. Marital Status Number (in thousands) Married 308 Widowed 58 Divorced 65 Never married 114 Determine the number of females 18 years old and older who are married or widowed.

Solve the problem. - $\text { Given that } P ( A ) = 0.35 , P ( B ) = 0.46 \text {, and } P ( A \cup B ) = 0.59 \text {, find } P ( A \cap B ) \text {. }$

Solve the problem. -The faculty at a college consists of 116 full-time teachers and 50 part-time teachers. Of the 116 full-time teachers, 57 are female. Of the 50 part-time teachers, 27 are female. Find the probability that a randomly Selected teacher is male or works part-time. A) $\frac { 109 } { 166 }$ B) $\frac { 43 } { 83 }$ C) $\frac { 66 } { 83 }$ D) $\frac { 23 } { 166 }$

Solve the problem. -A lottery game has balls numbered 1 through 19. What is the probability of selecting an even numbered ball or a 13? A) $\frac { 9 } { 10 }$ B) $\frac { 10 } { 19 }$ C) $\frac { 9 } { 19 }$ D) $\frac { 8 } { 19 }$

Solve the problem. -How many 6-symbol codes can be formed using 4 different symbols? Repeated symbols are allowed.

Solve the problem. -In a student survey, 97 students indicated that they speak Spanish, 30 students indicated that they speak French, 8 students indicated that they speak both Spanish and French, and 124 students indicated that they speak Neither. How many students participated in the survey?

onstruct a probability model for the experiment. -Rolling a 6-sided fair die twice

Use the information given in the figure. - How many are not in C?

Solve the problem. -How many arrangements of answers are possible in a multiple-choice test with 7 questions, each of which has 5 possible answers?

Solve the problem. -An environmental organization has 31 members. Each member will be placed on exactly 1 of 4 teams. Each team will work on a different issue. The first team has 4 members, the second has 9, the third has 10, and the Fourth has 8. In how many ways can these teams be formed? A) $2.219430350 \times 10 ^ { 26 }$ B) $8.222838654 \times 10 ^ { 33 }$ C) $6.453033770 \times 10 ^ { 15 }$ D) $5.162427016 \times 10 ^ { 16 }$

Solve the problem. -Suppose that the sample space is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and that outcomes are equally likely. Compute the probability of the event E = {1, 2, 4, 5, 7, 9, 10}. A) 7 B) $\frac { 7 } { 10 }$ C) $\frac { 7 } { 9 }$ D) $\frac { 4 } { 5 }$

Solve the problem. - $\text { If } n ( B ) = 24 , n ( A \cap B ) = 5 \text {, and } n ( A \cup B ) = 42 \text {, find } n ( A ) \text {. }$

Solve the problem. -In a survey about the number of siblings of college students, the following probability table was constructed: Number of Siblings Probability 0 0.24 1 0.32 2 0.19 3 0.14 4 or more 0.11 What is the probability that a student has less than 2 siblings?

Solve the problem. -In a survey of 55 hospital patients, 24 said they were satisfied with the nursing care, 26 said they were satisfied with the medical treatment, and 6 said they were satisfied with both. How many patients were satisfied with Neither? How many were satisfied with only the medical treatment?

Solve the problem. -A group of 7 friends goes bowling. How many different possibilities are there for the order in which they play if the youngest person is to bowl first?

Solve the problem. -The table below shows the results of a consumer survey of annual incomes in 100 households. Income Number of households \ 0-14,999 9 \ 15,000-24,999 23 \ 25,000-34,999 28 \ 35,000-44,999 30 \ 45,000 or more 10 What is the probability that a household has an annual income of $25,000 or more?

Solve the problem. -A die is weighted so that an even-numbered face is three times as likely to occur as an odd-numbered face. What probability should be assigned to each face?

Solve the problem. -A 6-sided die is rolled. What is the probability of rolling a number less than 3? A) $\frac { 1 } { 6 }$ В) $\frac { 1 } { 3 }$ C) $\frac { 1 } { 2 }$ D) $\frac { 2 } { 3 }$

Solve the problem. - Outcome Probability Red 0.22 Blue 0.27 Green 0.32 White 0.50

onstruct a probability model for the experiment. -Tossing one fair coin three times