MDM Exam Practice Exam Date:
1. Explain the differences between a bar graph and a histogram.
2. In how many ways can a student answer all of the questions on a true/false test that has eight questions? Explain your solution.
3. You are making a string of coloured balloons as a decoration for the formal. If you have five green, six gold, and four white balloons, in how many ways can you arrange them along the string?
4. Which row of Pascal’s triangle has terms that sum to 32?
5. There are 10 students on the basketball team, 11 students on the soccer team, and 14 students on the volleyball team. Only 3 students play on all three teams, but 5 students play both soccer and volleyball, 4 play both volleyball and basketball, and 7 play both soccer and basketball. What is the total number of students on the three teams? Illustrate your answer with a Venn diagram.
6. The Statsville hockey team has nine forwards, nine defenders, and two goalies. Use combinations to determine the number of ways the team can form a line-up of three forwards, two defenders, and one goalie.
7. The group organizing the Statsville College reunion includes 6 current students, 8 current staff members, and 11 alumni. Two individuals from each category will work on the publicity committee. Use combinations to determine the number of different publicity committees the group could form.
8. Two standard dice are rolled. What is the probability that the total of the two dice is less than 4?
9. Participants in marathons are often given numbers to wear, so that race officials can identify individual runners more easily. If the numbers are assigned randomly, what is the probability that the eight fastest runners will finish in the order of their assigned numbers, assuming that there are no ties?
10. A four-member curling team is randomly chosen from six grade-11 students and nine grade-12 students. What is the probability that the team has at least one grade-11 student?
11. If the probability of the Rangers defeating the Eagles in a hockey game is , what is the probability that the Rangers will win two consecutive games against the Eagles?
12. What is the key characteristic of a discrete variable?
13. Classify the following random variables as discrete or continuous.
a) the number of times a player bumps the ball in a volleyball game
b) the length of time a student spends doing homework
c) the volume of water in a swimming pool
d) the number of blue cars on a highway
14. Explain whether rolling a standard die is a probability experiment that has a uniform probability distribution.
15. Does the number of defective products in a random sample of 20 have a hypergeometric probability distribution? Explain why or why not.
17. What is the random variable in an exponential probability distribution?
20. To determine the general public’s vacation preferences, a tour company conducted a telephone survey of people randomly selected from a department store’s list of its credit-card holders. Describe the bias that could influence the results of this survey.
21. The usage of a hospital X-ray machine was monitored for 9 days. The data, rounded to the nearest hour, are listed below.
3, 13, 9, 10, 13, 21 ,12, 23, 13
a) Calculate the mean, median, and mode for these data.
b) Suggest a reason why you might want to exclude the lowest value from the calculations in parta).
22. You work as a health inspector and must visit each of the 15 restaurants in town once each week.
a) In how many different orders can you make these inspections?
b) If you were to work 50 weeks a year and use a different order every week, how long would it take you to try all of the different possible orders?
23. You have forgotten the combination to the lock for your locker. The combination consists of 3 different numbers from the set of 30 different numbers on the face of the lock.
a) What is the maximum number of combinations you would have to try to find your combination?
b) If it takes 30 s to try each combination, how long it would take, on average, to find the right one?
24. At a birthday party, the host has a party favour for each of the 12 guests. In how many ways can the host distribute the favours if
a) the favours are all different?
b) the host has half a dozen of each of two kinds of favours?
25. In how many ways can a 12-member soccer team share a half-time snack of four oranges, four apples, and four pears if each member takes one piece of fruit? Explain your reasoning.
26. For the upcoming musical, the director has auditioned eight singers suitable for the three male principal roles and ten singers suitable for the four female principal roles. In how many different ways can the director cast the principal roles for this show?
27. The students producing a school fashion show plan to have five scenes with music between them. The music students have come up with 18 pieces: 6 for piano, 5 for recorder, and 7 for guitar. The students want to use at least 1 piece for the piano. In how many ways can the group choose the 4 pieces of bridging music? Explain your reasoning.
28. Len just wrote a multiple-choice test with 15 questions, each having four choices. Len is sure that he got exactly 9 of the first 12 questions correct, but he guessed randomly on the last 3 questions. What is the probability that he will get at least 80% on the test?
29. At an athletic event, athletes are tested for steroids using two different tests. The first test has a 93.0% probability of giving accurate results, while the second test is accurate 87.0% of the time. For a sample that does contain steroids, what is the probability that
a) neither test shows that steroids are present?
b) both tests show that steroids are present?
c) at least one of the tests detects the steroids?
32. Suppose that Bayanisthol, a new drug, is effective for 65% of the participants in clinical trials. If a group of fifteen patients take this new drug,
a) what is the expected number of patients for whom the drug will be effective?
b) what is the probability that the drug will be effective for less than half of them?
33. Prepare a table and a graph of a hypergeometric distribution with n = 7, r = 2, and a = 4.
34. Five cards are dealt from a standard deck.
a) What is the probability that all five cards are diamonds?
b) What is the expected number of diamonds?