Exam 10: Counting and Probability

Solve the problem. -In a survey of 50 hospital patients, 24 said they were satisfied with the nursing care, 17 said they weresatisfied with the medical treatment, and 5 said they were satisfied with both. How many patients weresatisfied with neither? How many were satisfied with only the medical treatment?

Solve the problem. -A bag contains 2 red marbles, 7 blue marbles, and 8 green marbles. If one marble is selected at random,determine the probability that it is blue.

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

Solve the problem. -A hot dog stand sells hot dogs with cheese, relish, chili, tomato, onion, mustard, or ketchup. How manydifferent hot dogs can be concocted using any 5 of the extras?

Solve the problem. -In a survey of 137 vacationers in a popular beach resort town, 70 indicated they would consider buying ahome there, 62 would consider buying a beach villa, 57 would consider buying a lot, 27 would considerboth a home and a villa, 34 would consider both a home and a lot, 24 would consider both a villa and a lot,and 15 would consider all three. How many vacationers would not consider any of the three? How manywould consider only a home?

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

Find the value of the combination. -C(11, 8)

Solve the problem. -Lisa has 4 skirts, 8 blouses, and 2 jackets. How many 3-piece outfits can she put together assuming anypiece goes with any other?

Solve the problem. -A survey of 1,981 credit card users indicated that 911 had bought books online, 876 had bought musiconline, 439 had bought pet supplies online, 139 had bought both books and music, 200 had bought bothbooks and pet supplies, 160 had bought both music and pet supplies, and 93 had bought all three. Howmany credit card users did not buy any of the three? How many bought either books or pet supplies butnot music?

Solve the problem. -In the city of Gloomville, the probability of rain on New Yearʹs Day is 60%. What is the probability thatnext New Yearʹs Day it will not rain in Gloomville?

Write down all the subsets of the given set. -{3, 5, 9, 10}

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

Solve the problem. -How many 2-letter codes can be formed using the letters A, B, C, D, E, F, G, H, and I. Repeated letters areallowed.

Solve the problem. -List all the combinations of 6 objects a, b, c, d, e, and f taken 2 at a time. What is C(6, 2)?

Solve the problem. -The faculty at a college consists of 100 full-time teachers and 52 part-time teachers. Of the 100 full-timeteachers, 43 are female. Of the 52 part-time teachers, 30 are female. Find the probability that a randomlyselected teacher is male or works part-time.

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

Solve the problem. -A bag contains 8 red marbles, 2 blue marbles, and 1 green marble. What is the probability of choosing amarble that is red or green when one marble is drawn from the bag?

Determine whether the following is a probability model. -

Solve the problem. -Each of ten tickets is marked with a different number from 1 to 10 and put in a box. If you draw a ticketfrom the box, what is the probability that you will draw 1, 7, or 5?

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