Math 118 – Worksheet #04 - Probability

1. / A die with sixty sides is tossed once. Find the probability that a number divisible by is Round answer to 2 decimal places.
A) B) C) D) E)
2. / Determine the probability of the event.
You will roll a number different from 10 on a die.
A) B) 1 C) D)
3. / If you draw one card at random from a deck of 14 cards numbered 1 through 14, inclusive, what is the probability that the number you draw is divisible by 3?
A) B) C) D) E)
4. / From a deck of 52 ordinary playing cards, one card is drawn. What is the probability that it is a queen?
A) B) C) D) E)
5. / Determine the probability of the event.
You will draw a club from a standard deck of 52 playing cards.
A) B) C) D)
6. /
A) B) C) D) E)
7. / Suppose a fair coin is tossed 8 times. What is the probability of flipping exactly 3 heads?
A) B) C) D) E)
8. / Two regular six-sided dice are tossed. Find the probability that the sum will be
A) B) C) D) E)
9. / If a pair of dice, one green and one red, is rolled, what is the probability that the sum of the two dice is a number between 9 and 12, inclusive?
A) B) C) D) E)
10. / A spinner has 4 equal sectors colored yellow, blue, green, and red. If in 100 spins we get 29 blue (B), 22 red (R), 21 green (G), and 28 yellow (Y) outcomes, find the empirical probability of getting color P(G).
A) B) C) D) E)
11. / A fair die is rolled 4 times in succession. What is the probability that even numbers are rolled all 4 times? Round your answer to two decimal places.
A) 0.80 B) 0.04 C) 0.06 D) 0.75 E) 0.32
12. / A hat contains 24 names, 13 of which are female. If three names are randomly drawn from the hat, what is the probability that at least one male name is drawn?
A) 0.918 B) 0.859 C) 0.082 D) 0.141
13. / Helen and Patty both belong to a club of 25 members. A committee of 7 is to be selected at random from the 25 members. Find the probability that both Helen and Patty will be selected. Round your answer to 2 decimal places.
A) 0.11 B) 0.02 C) 0.51 D) 0.07 E) 0.25
14. / A bag contains 7 nickels, 2 dimes, and 5 quarters. If you draw 3 coins at random from the bag, without replacement, what is the probability that you will get a nickel, a quarter, and a nickel, in that order?
A) B) C) D) E)
15. / In a sample of 20 hand-held calculators, 11 are known to be nonfunctional. If 7 of these calculators are selected at random, what is the probability that exactly 5 in the selection are nonfunctional? Round to the nearest thousandth.
A) 0.714 B) 0.215 C) 0.550 D) 0.636 E) 0
16. / When printing color inserts for newspapers, it sometimes happens that the registration of the print colors is imperfect. (This results in the different colors not being aligned properly, so the image is blurry.) Suppose that in a run of 1707 one-page inserts, 68 have registration errors. If 12 inserts are chosen at random, what is the probability that at least one of them has a color registration error?
A) 0.3930 B) 0.6130 C) 0.6155 D) 0.3870
17. / A survey showed that 9% of high school football players later played football in college. Of these, 6% went on to play professional football. Find the probability that a randomly selected high school football player will play both collegiate and professional football.
A) 0.54% B) 15% C) 1.5% D) 0.054% E) 1.08%
18. / A coin is tossed and a die is rolled. What is the probability that the coin shows tails and the die shows 3?
A) B) C) D)
19. / A red ball and 9 white balls are in a box. If two balls are drawn, without replacement, what is the probability of getting a red ball on the first draw and a white ball on the second?
A) B) C) D) E)
20. / The tree measure below shows the probabilities associated with performance ratings given to a company’s employees. Assume 80 percent of the employees at the company received a satisfactory performance rating. What is the probability that a randomly chosen employee from the company has no previous experience and received a satisfactory performance rating?

A) 0.16 B) 0.72 C) 0.14 D) 0.28
21. / One ball is drawn at random from a bag containing 2 red balls and 13 white balls. What is the probability that the ball is green?
A) 0 B) C) D) E) 1
22. / One ball is drawn at random from a bag containing 10 red balls and 6 white balls. What is the probability that the ball is red or white?
A) 0 B) C) D) E) 1
23. / An urn contains two red balls numbered 1, 2, three white balls numbered 3, 4, 5, and two black balls numbered 6, 7. A ball is drawn from the urn. What is the probability that it is red or odd-numbered?
A) B) C) D) E)
24. / A spinner is numbered from 1 through 10. What is the probability of spinning a number less than 4 or greater than 7 in a single spin?
A) B) C) D)
25. / Two regular six-sided dice are tossed. Compute the probability of rollingor doubles.
A) B) C) D) E)
26. / Salaries.The following table gives the percent of employees of the Ace Company in each of three salary brackets, categorized by the sex of the employees. An employee is selected at random. What is the probability that the person is male or makes less than $30,000?
Earns
Less Than
$30,000 / Earns at Least
$30,000 and
Less Than
$50,000 / Earns
at Least
$50,000
Male / 33% / 11% / 5%
Female / 22% / 19% / 10%
A) 0.71 B) 0.55 C) 0.49 D) 1.04 E) 0.29
27. / AIDS deaths.The following table gives the numbers of AIDS deaths in a single year for people over age 13 in various categories. Use the table to find the probability, rounded to four decimal places, that a person who died of AIDS in this year was male or black (non-Hispanic).
White, non-
Hispanic / Black, non-
Hispanic / Hispanic / Other / Total
Male / 824 / 2406 / 607 / 165 / 4002
Female / 1140 / 1933 / 589 / 63 / 3725
A) 1.0795 B) 0.5179 C) 0.7681 D) 0.2319 E) 0.5615
28. / A traffic light follows the pattern green, yellow, red for 55, 9, and 15 seconds, respectively. What is the probability that a driver approaching this light will find it green or yellow? Round your answer to 2 decimal places.
A) 0.30 B) 0.02 C) 0.89 D) 0.08 E) 0.81
29. / A bag contains 3 red balls numbered 1, 2, 3, and 5 white balls numbered 4, 5, 6, 7, 8. One ball is drawn from the bag. What is the probability that the ball is red, given that the ball is even-numbered?
A) B) C) D) E)
30. / The table below lists the results of a survey of the students at a community college.
Females / Males / Total
Biology / 165 / 215 / 380
Chemistry / 230 / 185 / 415
Physiology / 255 / 225 / 480
Total / 650 / 625 / 1275
Find for a random selection from the surveyed students.
A) B) C) D)
31. / Two standard dice are thrown. Given that one of the dice shows a three, what is the probability that the sum on the two dice is three?
A) B) C) D) 0
32. / A college offers two sections of Physics 203 during the spring term, an early morning section (PH203a) and a late afternoon section (PH203b), which are taught by two different professors. The afternoon section has consistently had 70% of its students pass the course with a C or higher grade. The morning section’s rate has been 75%. Last term, 55% of the students in Physics 203 were enrolled in the morning class. If a randomly selected student from last term passed the class with a C or higher grade, what is the probability the student was in the morning class?
A) 0.5670 B) 0.5875 C) 0.7500 D) 0.3000
33. / Suppose past experience shows that 5% of school-age children in a certain geographic region have Attention Deficit Disorder (ADD). Assume that the probability of a doctor correctly diagnosing a child as having ADD is 77% and the probability of incorrectly diagnosing a child as having ADD is 4%. What is the probability that a child diagnosed as having ADD actually has the disorder?
A) 0.9600 B) 0.9615 C) 0.5033 D) 0.7700
34. / Assume that a person visiting Florida will visit Disney World, Busch Gardens, or both with probabilities 0.5, 0.3, and 0.1, respectively. Find the probability that a person visiting Florida will visit Busch Gardens, given that the person visited Disney World. Round your answer to 2 decimal places.
A) 0.20 B) 0.33 C) 0.60 D) 1.67 E) 5.00
35. / Military spending. Suppose the following table summarizes the opinions of various groups on the issue of increased military spending.
Whites / Nonwhites / Total
Opinion / Reps. Dems. / Reps. Dems.
Favor / 285 70 / 40 / 55 / 450
Oppose / 115 280 / 10 / 145 / 550
Total / 400 350 / 50 / 200 / 1000
Given that a randomly selected individual is nonwhite, find the probability that he or she opposes increased military spending.
A) B) C) D) E)
36. / Universal health care.The following table gives the results of a 2005 survey of 1000 people regarding the funding of universal health care by employers (employer mandate).
Favor / Oppose / No Opinion / Total
Democrat / 275 / 120 / 25 / 420
Republican / 160 / 375 / 45 / 580
Total / 435 / 495 / 70 / 1000
What is the probability that a person selected at random from this group will favor universal health care with an employer mandate, given that the person is a Democrat?
A) B) C) D) E)
37. / A drawer contains 4 red socks, 2 white socks, and 2 blue socks. Without looking, you draw out a sock, return it, and draw out a second sock. What is the probability that the first sock is white and the second sock is white?
A) B) C) D) 1
38. / When three coins are tossed, the probability of getting 3 tails is and the probability of 3 heads is also . The probability of 2 tails and 1 head is and the probability of 2 heads and 1 tail is also . What is the probability of repeatedly tossing a group of three coins and getting 2 tails and 1 head 5 times in succession?
A) B) C) D)
39. / A die is rolled 6 times. What is the probability of rolling an odd number each time?
A) B) C) D) E)
40. / Two bags each contain red marbles and green marbles. The first bag contains 2 red marbles and 4 green marbles and the second bag contains 4 red marbles and 2 green marbles. A marble is randomly drawn from each bag. What is the probability that both marbles are green?
A) B) C) D)
41. / A company has estimated that the probabilities of success for three products introduced in the market are , , and , respectively. Assuming independence, find the probability that none of the products is successful?
A) B) C) D) E)
42. / A coin is tossed and a die is rolled. What is the probability that the coin shows tails and the die shows 1?
A) B) C) D)

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