Exam 10: Counting and Probability

Solve the problem. -A bag contains 6 red marbles, 3 blue marbles, and 1 green marble. What is the probability of choosing amarble that is not blue when one marble is drawn from the bag?

Determine whether the following is a probability model. -

Solve the problem. -A restaurant offers a choice of 4 salads, 7 main courses, and 2 desserts. How many possible 3-coursemeals are there?

Solve the problem. -In a student survey, 119 students indicated that they speak Spanish, 25 students indicated that they speakFrench, 9 students indicated that they speak both Spanish and French, and 122 students indicated thatthey speak neither. How many students participated in the survey?

Solve the problem. -From 8 names on a ballot, a committee of 5 will be elected to attend a political national convention. Howmany different committees are possible?

Write the word or phrase that best completes each statement or answers the question. Construct a probability model for the experiment. -Spinner I has 4 sections of equal area, numbered 1, 2, 3, and 4. Spinner II has 3 sections of equal area,labeled Red, Yellow, and Green. Spinner III has 2 sections of equal area labeled A and B. Spin Spinner I,then Spinner II, then Spinner III.What is the probability of getting a 2, followed by Yellow or Green, followed by B?

Solve the problem. -How many different 10-letter words (real or imaginary)can be formed from the letters in the wordPHILOSOPHY?

Solve the problem. -How many 3-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 if the first digitcannot be 0? Repeated digits are allowed.

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 = 2, 10 .

Find the value of the permutation. -P(4, 0)

Solve the problem. -How many different license plates can be made using 3 letters followed by 2 digits selected from the digits0 through 9, if letters and digits may be repeated?

Solve the problem. -A coin is weighted so that heads is 14 times as likely as tails to occur. What probability should be assignedto heads? to tails?

Solve the problem. -The following data represent the marital status of females 18 years and older in a certain U.S. city. Determine the number of females 18 years old and older who are married or widowed.

Solve the problem. -If n(A)= 27, n(B)= 42, and n = 4, find n

Solve the problem. -Two 6-sided dice are rolled. What is the probability the sum of the two numbers on the dice will be 6?

Write the word or phrase that best completes each statement or answers the question. Construct a probability model for the experiment. -Rolling a 6-sided fair die once

Solve the problem. -How many 5-card poker hands consisting of three 7ʹs and two cards that are not 7ʹs are possible in a52-card deck?

Solve the problem. -If n(A)= 46, n(B)= 45, and n( = 85, find n

Write the word or phrase that best completes each statement or answers the question. Construct a probability model for the experiment. -Tossing two fair coins once

Solve the problem. -How many ways are there to choose a soccer team consisting of 3 forwards, 4 midfield players, and 3defensive players, if the players are chosen from 10 forwards, 7 midfield players, and 5 defensive players?