Exam 12: Counting and Probability

Choose the one alternative that best completes the statement or answers the question. -What is the probability that at least 2 people have the same birth month in a group of 4 people?

Choose the one alternative that best completes the statement or answers the question. -Find the probability of having 4 girls in a 4 -child family.

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? ,

Choose the one alternative that best completes the statement or answers the question. -Given that $P ( A ) = 0.35 , P ( B ) = 0.46$ , and $P ( A \cup B ) = 0.59$ , find $P ( A \cap B )$ .

Write down all the subsets of the given set. - $\{ 2 , \alpha , 6 , \pi \}$

Choose the one alternative that best completes the statement or answers the question. -Suppose that the sample space is $\mathrm { S } = \{ 1,2,3,4,5,6,7,8,9,10 \}$ and that outcomes are equally likely. Compute the probability of the event E: "a number divisible by 3 ".

Choose the one alternative that best completes the statement or answers the question. -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?

Write the word or phrase that best completes each statement or answers the question. Construct a probability model for the experiment. -Tossing a fair coin twice given that the coin is weighted so that heads is three times as likely as tails to occur.

Choose the one alternative that best completes the statement or answers the question. -Given that $\mathrm { P } ( \mathrm { A } ) = 0.15 , \mathrm { P } ( \mathrm { B } ) = 0.42$ , and $\mathrm { P } ( \mathrm { A } \cap \mathrm { B } ) = 0.10$ , find $\mathrm { P } ( \mathrm { A } \cup \mathrm { B } )$

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?

Use the information given in the figure. - How many are in $A$ or $B$ or $C$ ?

Choose the one alternative that best completes the statement or answers the question. -A bag contains 5 red marbles, 3 blue marbles, and 1 green marble. What is the probability of choosing a marble that is not blue when one marble is drawn from the bag?

Choose the one alternative that best completes the statement or answers the question. -A bag contains 9 red marbles, 3 blue marbles, and 7 green marbles. If one marble is selected at random, determine the probability that it is blue.

Solve the problem. -A hot dog stand sells hot dogs with cheese, relish, chili, tomato, onion, mustard, or ketchup. How many different hot dogs can be concocted using any 3 of the extras?

Solve the problem. -In a survey of 421 computer buyers, 213 put price as a main consideration, 205 put performance as a main consideration, and 57 listed both price and performance. How many computer buyers listed other Considerations? How many looked only for performance?

Write the word or phrase that best completes each statement or answers the question. -How many different 11-letter words (real or imaginary) can be formed from the letters of the word MISSISSIPPI? Leave your answer in factorial form.

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?

Find the value of the permutation. -P(9, 1)

Determine whether the following is a probability model. - Outcome Probability Red 0.17 Blue 0.30 Green 0.33 White 0.20

Determine whether the following is a probability model. - Outcome Probability Red 0.22 Blue 0.27 Green 0.32 White 0.50