Business Math Exam 2 Questions
A raffle offers a first prize of $300 and 3 second prizes of $70 each. One ticket costs $2, and 400 tickets are sold. Find the expected payback for a person who buys 1 ticket. Is this a fair game? The expected payback for a person who buys 1 ticket is $(a)_____. (Round to two decimal places as needed.) Is this a fair game? The raffle (b)_____ a fair game because the expected payback of the game (c)_____ $0.
(a) -. 73. (b) is not (c) is not equal to
47. At a conference promoting excellence in education for African Americans in Detroit, special-edition books were selected to be given away in contests. There were 9 books written by Langston Hughes, 5 books by James Baldwin, and 7 books by Toni Morrison. The judge of one contest selected 6 books at random for prizes. Find the probabilities that the selection consisted of the following. (a) 3 Hughes and 3 Morrison books (b) Exactly 4 Baldwin books (c) 2 Hughes, 3 Baldwin, and 1 Morrison book (d) At least 4 Hughes books (e) Exactly 4 books written by males (Morrison is female) (f) No more than 2 books written by Baldwin
(a) 0.0542 (b) 0.0111 (c) 0.0464 (d) 0.1827 (e) 0.3874 (f) 0.8854
An assembly-line machine turns out washers with the following thicknesses (in millimeters). Find the mean and standard deviation of the thicknesses. 1.27, 1.21, 1.65, 1.89, 1.93, 1.36, 1.63, 1.22, 1.35, 1.55, 1.79, 1.55, 2.07, 1.49, 1.73, 1.43 The mean is (a)_____ mm. (Round to four decimal places as needed.) The standard deviation is (b)_____ mm. (Use the answer for the mean to find this answer. Round to four decimal places as needed.)
(a) 1.57 (b) .2617
41. A concert to raise money for an economics prize is to consist of 5 works: 2 overtures, 2 sonatas, and a piano concerto. (a) In how many ways can the program be arranged? (b) In how many ways can the program be arranged if an overture must come first?
(a) 120 (b) 48
45. Five orchids from a collection of 20 are to be selected for a flower show. (a) In how many ways can this be done? (b) In how many ways can the 5 be selected if 2 special plants from the 20 must be included?
(a) 15,504 (b) 816
For many years, a state used 1 letter followed by 5 digits on its automobile license plates. Complete parts (a) through (c) below. (a) How many different license plates are possible with this arrangement? (Use scientific notation. Use the multiplication symbol in the math palette as needed. Round to three decimal places as needed.) (b) When the state ran out of new numbers, the order was reversed to 5 digits followed by 1 letter. How many new license plate numbers were then possible? (Use scientific notation. Use the multiplication symbol in the math palette as needed. Round to three decimal places as needed.) (c) Eventually, the numbers described in part (b) were also used up. The state then issued plates with 1 digit followed by 1 letter and then 5 digits. How many new license plate numbers will this provide? (Use scientific notation. Use the multiplication symbol in the math palette as needed. Round to three decimal places as needed.)
(a) 2.6 x 10^6 (b) 2.6 x 10^6 (c) 2.6 x 10^7
A local travel office has 10 employees. Their monthly salaries are given below. $1550, $1710, $1660, $1220, $1420, $1620, $1840, $1300, $3800, $5800 (a) Find the mean. The mean is $_____. (b) Find the median. The median is $_____.
(a) 2192 (b) 1640
45. At the first meeting of a committee to plan a Northern California pow-wow, there were 3 women and 3 men from the Miwok tribe, 3 women and 2 men from the Hoopa tribe, and 4 women and 5 men from the Pomo tribe. If the ceremony subcouncil consists of 5 people and is randomly selected, find the probabilities that the subcouncil contains the following: (a) 3 men and 2 women; (b) exactly 3 Miwoks and 2 Pomos; (c) 2 Miwoks, 2 Hoopas, and a Pomo; (d) 2 Miwoks, 2 Hoopas, and 2 Pomos; (e) more women than men; (f) exactly 3 Hoopas; (g) at least 2 Pomos.
(a) 225/646 (b) 15/323 (c) 225/2584 (d) 0 (e) 1/2 (f) 175/2584 (g) 503/646
43. How many different 4-letter radio station call letters can be made if (a) the first letter must be K or W and no letter may be repeated? (b) repeats are allowed, but the first letter is K or W? (c) the first letter is K or W, there are no repeats, and the last letter is R?
(a) 27,600 (b) 35,152 (c) 1104
51. A certain website requires users to log on using a security password. (a) If passwords must consist of six letters, followed by a single digit, determine the total number of possible distinct passwords. (b) If passwords must consist of six non-repetitive letters, followed by a single digit, determine the total number of possible distinct passwords.
(a) 3,089,157,760 (b) 1,657,656,000
23. Kelly Clark has different books to arrange on a shelf: 4 blue, 3 green, and 2 red. (a) In how many ways can the books be arranged on a shelf? (b) If books of the same color are to be grouped together, how many arrangements are possible? (c) In how many distinguishable ways can the books be arranged if books of the same color are identical but need not be grouped together? (d) In how many ways can you select 3 books, one of each color, if the order in which the books are selected does not matter? (e) In how many ways can you select 3 books, one of each color, if the order in which the books are selected matters?
(a) 362,880 (b) 1728 (c) 1260 (d) 24 (e) 144
33. A local television station has eleven slots for commercials during a special broadcast. Six restaurants and 5 stores have bought slots for the broadcast. (a) In how many ways can the commercials be arranged? (b) In how many ways can the commercials be arranged so that the restaurants are grouped together and the stores are grouped together? (c) In how many ways can the commercials be arranged so that the restaurant and store commercials are alternating?
(a) 39,916,800 (b) 172,800 (c) 86,400
33. Hamburger Hut sells regular hamburgers as well as a larger burger. Either type can include cheese, relish, lettuce, tomato, mustard, or catsup. (a) How many different hamburgers can be ordered with exactly three extras? (b) How many different regular hamburgers can be ordered with exactly three extras? (c) How many different regular hamburgers can be ordered with at least five extras?
(a) 40 (b) 20 (c) 7
41. Five cards are chosen from an ordinary deck to form a hand in poker. In how many ways is it possible to get the following results? (a) 4 queens (b) No face card (c) Exactly 2 face cards (d) At least 2 face cards (e) 1 heart, 2 diamonds, and 2 clubs
(a) 48 (b) 658,008 (c) 652,080 (d) 844,272 (e) 79,092
Five cards are chosen at random from an ordinary deck to form a hand in poker. In how many ways is it possible to get the following results? Complete parts (a) through (e) below. (a) How many ways is it possible to choose 4 nines? There are _____ ways. (b) How many ways is it possible to choose no clubs? There are _____ ways. (c) How many ways is it possible to choose exactly 3 clubs? There are _____ ways. (d) How many ways is it possible to choose at least 3 clubs? There are _____ ways. (e) How many ways is it possible to choose 1 spade, 1 club, and 3 hearts? There are _____ ways.
(a) 48 (b) 575757 (c) 211926 (d) 241098 (e) 48334
31. A salesperson has the names of 6 prospects. (a) In how many ways can she arrange her schedule if she calls on all 6? (b) In how many ways can she arrange her schedule if she can call on only 4 of the 6?
(a) 720 (b) 360
39. Salespeople of a large corporation received an annual bonus based upon their sales performance. The size of the bonuses was normally distributed with a mean of $12,000 and a standard deviation of $2500. (a) What percent of the salespeople received an annual bonus in excess of $10,000? (b) What percent of the salespeople received an annual bonus between $10,000 and $15,000? (c) What size bonus is exceeded by 75% of all other bonuses? (d) Find the smallest and largest amounts for the middle 75% of the annual bonuses.
(a) 78.81% (b) 67.31% (c) $10,314 (d) $9124; $14,876
37. A legislative committee consists of 5 Democrats and 4 Republicans. A delegation of 3 is to be selected to visit a small Pacific island republic. (a) How many different delegations are possible? (b) How many delegations would have all Democrats? (c) How many delegations would have 2 Democrats and 1 Republican? (d) How many delegations would include at least 1 Republican?
(a) 84 (b) 10 (c) 40 (d) 74
21. Find the number of distinguishable permutations of the letters in each word. (a) initial (b) little (c) decreed
(a) 840 (b) 180 (c) 420
45. A raffle offers a first prize of $400 and 3 second prizes of $300 each, and 20 third prizes of $10 each. If 10,000 tickets are sold at 50 cents each, find the expected payback for a person buying 1 ticket. Is this a fair game?
-$0.72; no
47. A state lottery requires you to choose 4 cards from an ordinary deck: 1 heart, 1 club, 1 diamond, and 1 spade in that order from the 13 cards in each suit. If all four choices are selected by the lottery, you win $5000. It costs $1 to play.
-$0.82
A bridge hand consists of 13 cards from a deck of 52. Find the probability that a bridge hand includes exactly 4 aces and exactly 3 kings. The probability is _____. (Round to six decimal places as needed.)
. 000044
Suppose that 3 cards are drawn from a well-shuffled deck of 52 cards. What is the probability that all 3 are spades? The probability is _____. (Simplify your answer. Type an integer or decimal rounded to the nearest thousandth as needed.)
. 013
A container contains 10 diesel engines. The company chooses 5 engines at random, and will not ship the container if any of the engines chosen are defective. Find the probability that a container will be shipped even though it contains 2 defective engines. The probability the container will be shipped is _____. (Round to the nearest thousandth as needed.)
. 222
Claudia is arranging seating for her sorority's fall banquet. She has to sit 7 seniors, 5 juniors, 9 sophomores 3 freshmen at the head banquet table. What is the probability members of the same class will all sit together?
.0000000000509 Solution (4 * 7! * 3 * 5! * 2 * 9! * 3!) / 24! = .0000000000509
A bridge hand is made up of 13 cards from a deck of 52. Find the probability that a hand chosen at random contains at least 3 fives. The probability that a bridge hand chosen at random contains at least 3 fives is _____. (Round to four decimal places as needed.)
.0438
Smooth ASAP is planning a big concert for this weekend. He has 5 friends, Sydni, Val, Jake, RJ and Hayden, who want to come to his concert and sit front row. What is the probability RJ and Sydni sit by each other?
.4 Solution (2! 4!) / 5! = .4
5. In a club with 9 male and 11 female members, a 5-member committee will be randomly chosen. Find the probability that the committee contains the following. All men
0.008127
57. A bridge hand is made up of 13 cards from a deck of 52. Find the probabilities that a hand chosen at random contains the following. Exactly 2 aces and exactly 2 kings
0.0402
29. A box of oatmeal must contain 16 oz. The machine that fills the oatmeal boxes is set so that, on the average, a box contains 16.5 oz. The boxes filled by the machine have weights that can be closely approximated by a normal curve. What fraction of the boxes filled by the machine are underweight if the standard deviation is as follows? 0.5 oz
0.1587
9. In a club with 9 male and 11 female members, a 5-member committee will be randomly chosen. Find the probability that the committee contains the following. At least 4 women
0.2214
41. A machine that fills quart milk cartons is set up to average 32.2 oz per carton, with a standard deviation of 1.2 oz. What is the probability that a filled carton will contain less than 32 oz of milk?
0.4338
21. Twenty-six slips of paper are each marked with a different letter of the alphabet and placed in a basket. A slip is pulled out, its letter recorded (in the order in which the slip was drawn), and the slip is replaced. This is done 5 times. Find the probabilities that the following "words" are formed. A word with no repetition of letters
0.6644
Decide whether the exercise involves permutations or combinations, and then solve the problem. Marbles are being drawn without replacement from a bag containing 10 marbles. (a) How many samples of 3 marbles can be drawn? (b) How many samples of 4 marbles can be drawn? (c) If the bag contains 2 yellow, 2 white, and 6 blue marbles, how many samples of 2 marbles can be drawn in which all marbles are blue? Does the problem involve permutations or combinations? 1. Permutations 2. Combinations (a) How many samples of 3 marbles can be drawn? _____ samples (b) How many samples of 4 marbles can be drawn? _____ samples (c) If the bag contains 2 yellow, 2 white, and 6 blue marbles, how many samples of 2 marbles can be drawn in which all marbles are blue? _____ samples
2. Combinations (a) 120 (b) 210 (c) 15
Decide whether the exercise involves permutations or combinations, and then solve the problem. In a club with 10 male and 11 female members, how many 7-member committees can be chosen that have (a) all men? (b) all women? (c) 4 men and 3 women? Does the problem involve permutations or combinations? 1. Permutations 2. Combinations (a) There can be _____ all male committees. (b) There can be _____ all female committees. (c) There can be _____ 7-member committees with 4 men and 3 women.
2. Combinations (a) 120 (b) 330 (c) 34650
13. Find the expected value for the random variable x having the probability function shown in each graph. x P(x) 1 0.2 2 0.3 3 0.1 4 0.4
2.7
15. A couple has narrowed down the choice of a name for their new baby to 4 first names and 5 middle names. How many different first- and middle-name arrangements are possible?
20
39. A shipment of 11 printers contains 2 that are defective. Find the probability that a sample of the following sizes, drawn from the 11, will not contain a defective printer. 4
21/55
Find the expected value for the random variable x whose probability function graph is displayed here. x P(x) 1 0.25 2 0.2 3 0.1 4 0.15 5 0.3 What is the expected value of the random variable? (Round to the nearest hundredth as needed.)
3.05
Claudia is arranging seating for her sorority's fall banquet. She has to sit 7 seniors, 5 juniors, 9 sophomores and 3 freshmen at the head banquet table. If members of the same class must sit together, in how many ways can she do this?
3.1604 * 10^13 Solution 4 * 7! * 3 * 5! * 2 * 9! * 3! = 3.1604 * 10^13
39. A baseball team has 19 players. How many 9-player batting orders are possible?
3.352 * 10^10
Find the expected value of the random variable. x P(x) 2 0.3 3 0.2 4 0.1 5 0.4 What is the expected value? (Type an integer or a decimal.)
3.6
A used-car dealer gets complaints about his cars as shown in the table. Number of Complaints per day Probability 0 0.01 1 0.05 2 0.14 3 0.22 4 0.38 5 0.1 6 0.1 Find the expected number of complaints per day. The expected number of complaints per day is _____. (Type an integer or a decimal. Do not round your answer.)
3.61
23. From a group of 3 women and 5 men, a delegation of 2 is selected. Find the expected number of women in the delegation.
3/4
13. Find the probability that the 2-card hand described above contains the following. At least 1 ace
33/221
29. From a group of 8 newly hired office assistants, 3 are selected. Each of these 3 assistants will be assigned to a different manager. In how many ways can they be selected and assigned?
336 Solution 8 npr 3 = 336
A couple has narrowed down the choices of a name for their new baby to 5 first names and 7 middle names. How many different first- and middle-name arrangements are possible? There are _____ different possible first- and middle-name arrangements. (Type a whole number.)
35
13. How many different types of homes are available if a builder offers a choice of 6 basic plans, 3 roof styles, and 2 exterior finishes?
36
37. A shipment of 11 printers contains 2 that are defective. Find the probability that a sample of the following sizes, drawn from the 11, will not contain a defective printer. 2
36/55
A shipment of 11 printers contains 2 that are defective. Find the probability that a sample of size 2, drawn from the 11, will not contain a defective printer. The probability is _____. (Type an integer or a simplified fraction.)
36/55
35. The chickens at Colonel Thompson's Ranch have a mean weight of 1850 g, with a standard deviation of 150 g. The weights of the chickens are closely approximated by a normal curve. Find the percent of all chickens having weights in the following ranges. Between 1750 and 1900 g
37.81%
In an experiment on social interaction, 11 people will sit in 11 seats in a row. In how many ways can this be done? There are _____ ways 11 people can sit in 11 seats in a row. (Type a whole number.)
39916800
35. From a group of 16 smokers and 22 nonsmokers, a researcher wants to randomly select 8 smokers and 8 nonsmokers for a study. In how many ways can the study group be selected?
4,115,439,900
15. Find the probability that the 2-card hand described above contains the following. 2 cards of the same suit
4/17
Natalie is planning her outfit for a hot date. She has 3 shirts, 7 pairs of pants, 4 pairs of shoes and 5 different accessories to choose from. If she can only wear one of each of these, how many different outfits can she make?
420 Solution 3 * 7 * 4 * 5 = 420
Smooth ASAP is planning a big concert for this weekend. He has 5 friends, Sydni, Val, Jake, RJ and Hayden, who want to come to his concert and sit front row. How many ways can he arrange his friends if RJ and Sydni must sit by each other?
48 Solution 2 * 4! = 48
Mixed in a drawer are 4 blue socks, 8 white socks, and 6 gray socks. You pull out two socks, one at a time, without looking. Find the probability of getting 2 socks of the same color. The probability of getting 2 socks of the same color is _____. (Type an integer or a simplified fraction.)
49/153
Find the number of distinguishable ways to arrange the letters in the word "mathematics".
4989600 Solution 11! / (2! 2! 2!) = 4989600
43. If a baseball coach has 5 good hitters and 4 poor hitters on the bench and chooses 3 players at random, in how many ways can he choose at least 2 good hitters?
50
37. The chickens at Colonel Thompson's Ranch have a mean weight of 1850 g, with a standard deviation of 150 g. The weights of the chickens are closely approximated by a normal curve. Find the percent of all chickens having weights in the following ranges. More than 2100 g or less than 1550 g
7.05%
1. A basket contains 7 red apples and 4 yellow apples. A sample of 3 apples is drawn. Find the probabilities that the sample contains the following. All red apples
7/33
55. A teach gives a test to a large group of students. The results are closely approximated by a normal curve. The mean is 76, with a standard deviation of 8. The teacher wishes to give A's to the top 8% of the students and F's to the bottom 8%. A grade of B is given to the next 20%, with D's given similarly. All other students get C's. Find the bottom cutoff (rounded to the nearest whole number) for the following grades. C
71
37. In an experiment on social interaction, 6 people will sit in 6 seats in a row. In how many ways can this be done?
720
19. Twenty-six slips of paper are each marked with a different letter of the alphabet and placed in a basket. A slip is pulled out, its letter recorded (in the order in which the slip was drawn), and the slip is replaced. This is done 5 times. Find the probabilities that the following "words" are formed. Chuck
8.417 * 10^-8 Solution 1^5/26^5
51. The game of Sets uses a special deck of cards. Each card has one, two, or three identical shapes, all of the same color and style. There are three possible shapes: squiggle, diamond, and oval. There are three possible colors: green, purple, and red. There are three possible styles: solid, shaded, or outline. The deck consists of all possible combinations of shape, color, style, and number of shapes. How many cards are in the deck?
81 Solution 3^4 = 81
33. The chickens at Colonel Thompson's Ranch have a mean weight of 1850 g, with a standard deviation of 150 g. The weights of the chickens are closely approximated by a normal curve. Find the percent of all chickens having weights in the following ranges. More than 1700 g
84.13%
53. A teach gives a test to a large group of students. The results are closely approximated by a normal curve. The mean is 76, with a standard deviation of 8. The teacher wishes to give A's to the top 8% of the students and F's to the bottom 8%. A grade of B is given to the next 20%, with D's given similarly. All other students get C's. Find the bottom cutoff (rounded to the nearest whole number) for the following grades. A
87
A bag contains 3 red apples and 3 yellow apples. 3 apples are selected at random. Find the probability of selecting 1 red apple and 2 yellow apples. The probability is _____. (Type an integer or a simplified fraction.)
9/20
19. Suppose 3 marbles are drawn without replacement from a bag containing 3 yellow and 4 white marbles. What is the expected number of yellow marbles in the sample?
9/7
From a group of 17 smokers and 27 nonsmokers, a researcher wants to randomly select 6 smokers and 6 nonsmokers for a study. In how many ways can the study group be selected? How many ways can the group be selected? A. 3,663,419,760 B. 2,637,662,227,200 C. 49,830,215,138,704 D. 1,899,116,803,584,000
A. 3,663,419,760
Find the mode(s) for the following group of data items. 37, 34, 33, 32, 38, 35, 31, 33 Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The mode(s) is/are _____. (Use a comma to separate answers as needed.) B. There is no mode.
A. 33
23. A bag contains 5 black, 1 red, and 3 yellow jelly beans: you take 3 at random. How many samples are possible in which the jelly beans are (a) all black? (b) all red? (c) all yellow? (d) 2 black and 1 red? (e) 2 black and 1 yellow? (f) 2 yellow and 1 black? (g) 2 red and 1 yellow?
Combinations (a) 10 (b) 0 (c) 1 (d) 10 (e) 30 (f) 15 (g) 0
21. Marbles are being drawn without replacement from a bag containing 16 marbles. (a) How many samples of 2 marbles can be drawn? (b) How many samples of 4 marbles can be drawn? (c) If the bag contains 3 yellow, 4 white, and 9 blue marbles, how many samples of 2 marbles can be drawn in which both marbles are blue?
Combinations (a) 120 (b) 1820 (c) 36
17. In a club with 9 male and 11 female members, how many 5-member committees can be chosen that have (a) all men? (b) all women? (c) 3 men and 2 women?
Combinations (a) 126 (b) 462 (c) 4620
19. In a game of musical chairs, 12 children will sit in 11 chairs arranged in a row (one will be left out). In how many ways can this happen, if we count rearrangements of the children in the chairs as different outcomes?
Permutations; 479,001,600
A group of 10 workers decides to send a delegation of 3 to their supervisor to discuss their grievances. Complete parts (a) through (c) below. (a) How many delegations are possible? There are _____ delegations possible. (b) If it is decided that a particular worker must be in the delegation, how many different delegations are possible? There are _____ delegations possible. (c) If there are 3 women and 7 men in the group, how many delegations would include at least 1 woman? There are _____ delegations possible.
(a) 120 (b) 36 (c) 85
A legislative committee consists of 4 Democrats and 7 Republicans. A delegation of 4 is to be selected to visit a small island republic. Complete parts (a) through (d) below. (a) How many different delegations are possible? The 4 delegates can be selected _____ different ways. (b) How many delegations would have all Democrats? The 4 delegates can be selected _____ different ways if all 4 are Democrats. (c) How many delegations would have 3 Democrats and 1 Republican? The 4 delegates can be selected _____ different ways if 3 are Democrats and 1 is a Republican. (d) How many delegations would include at least 1 Republican? The 4 delegates can be selected _____ different ways if at least 1 is a Republican.
(a) 330 (b) 1 (c) 28 (d) 329
Find the number of distinguishable permutations of the letters in each word below. (a) palace (b) Kansas (c) referred (a) The number of distinguishable permutations is _____. (Simplify your answer.) (b) The number of distinguishable permutations is _____. (Simplify your answer.) (c) The number of distinguishable permutations is _____. (Simplify your answer.)
(a) 360 (b) 180 (c) 1120
11. In how many ways can a hand of 6 clubs be chosen from an ordinary deck?
1716
Decide whether the exercise involves permutations or combinations, and then solve the problem. A bag contains 5 black, 1 red, and 4 yellow jelly beans; you take 4 at random. How many samples are possible in which the jelly beans are the following. (a) all black? (b) all red? (c) all yellow? (d) 3 black and 1 red? (e) 3 black and 1 yellow? (f) 3 yellow and 1 black? (g) 3 red and 1 yellow? Does the problem involve permutations or combinations? 1. Combinations 2. Permutations (a) In how many ways can 4 jelly beans be chosen so all are black? _____ samples (b) In how many ways can 4 jelly beans be chosen so all are red? _____ samples (c) In how many ways can 4 jelly beans be chosen so all are yellow? _____ samples (d) In how many ways can 4 jelly beans be chosen so that 3 are black and 1 is red? _____ samples (e) In how many ways can 4 jelly beans be chosen so that 3 are black and 1 is yellow? _____ samples (f) In how many ways can 4 jelly beans be chosen so that 3 are yellow and 1 is black? _____ samples (g) In how many ways can 4 jelly beans be chosen so that 3 are red and 1 is yellow? _____ samples
1. Combinations (a) 5 (b) 0 (c) 1 (d) 10 (e) 40 (f) 20 (g) 0
Matt must make a new code for the lock to his deer lease. It must consist of 3 letters, followed by 5 digits, then 2 letters and 1 more digit. The first letter must be a vowel and the middle digit of the first 5 must be even. If no letter or digit can be repeated, how many code words can be formed?
1.1476 * 10^11 Solution 5 * 22 * 23 * 5 * 6 * 5 * 7 * 8 * 24 * 25 *9 = 1.1476 * 10^11
55. A bridge hand is made up of 13 cards from a deck of 52. Find the probabilities that a hand chosen at random contains the following. Only hearts
1.575 * 10^-12
A bag contains 6 red balls and 4 blue balls. If 4 balls are selected at random, find the probability of selecting 4 red balls. The probability is _____. (Type an integer or a simplified fraction.)
1/14
25. If 2 cards are drawn at one time from a deck of 52 cards, what is the expected number of diamonds?
1/2
43. Dan LaChapelle has the name of 6 prospects, including a customer in Scottsdale. He randomly arranges his schedule to call on only 4 of the 6 prospects. Find the probability that the customer from Scottsdale is not called upon.
1/3
Find the mean of the quiz scores in the table to the right. x P(x) 8 3 9 2 11 5 12 3 The mean is _____. (Round to the nearest tenth.)
10.2
49. The U.S. Postal Service currently uses 5-digit zip codes in most areas. How many zip codes are possible if there are no restrictions on the digits used? How many would be possible if the first number could not be 0?
100,000; 90,000
Suppose that 3 cards are drawn from a well-shuffled deck of 52 cards. What is the probability that all 3 are diamonds? The probability is P(E) = _____. (Type an integer or a simplified fraction.)
11/850
Kristen's financial advisor has given her a list of 12 potential investments and has asked her to select and rank her favorite four. In how many different ways can she do this? There are _____ different ways Kristen can rank the four investments. (Type a whole number.)
11880
For the following set of numbers, find the median. 11, 13, 24, 9, 24, 14, 10 The median is _____.
13
29. After studying all night for a final exam, a bleary-eyed student randomly grabs 2 socks from a drawer containing 9 black, 6 brown, and 2 blue socks, all mixed together. What is the probability that she grabs a matched pair?
13/34
17. Find the probability that the 2-card hand described above contains the following. No face cards
130/221
11. Two cards are drawn at random from an ordinary deck of 52 cards. How many 2-card hands are possible?
1326
11. Find the expected value for each random variable. z P(z) 9 0.14 12 0.22 15 0.38 18 0.19 21 0.07
14.49
For the following set of numbers, find the mean. 10.8, 12.8, 23.8, 8.8, 23.8, 13.8, 9.8 The mean is _____.
14.8
3. A basket contains 7 red apples and 4 yellow apples. A sample of 3 apples is drawn. Find the probabilities that the sample contains the following. 2 yellow and 1 red apple
14/55
Michael has 7 green, 3 red and 9 blue M&Ms. If he selects 5 M&Ms: a. What is the probability he will select at least 2 blue M&Ms? b. What is the probability he will select exactly one blue and one red M&M? c. What is the probability he will get exactly 4 of the same color?
a. .8158 Solution 11628 - {[c(9, 0) * c(10, 5)] + [c(9, 1) * c(10, 4)]} / 11628 = .8158 b. .0813 Solution [c(9, 1) * c(3, 1) * c(7, 3)] / 11628 = .0813 c. .1445 Solution {[c(7, 4) * c(12, 1)] + [c(9, 4) * c(10, 1)]} / 11628 = .1445
How many different 6-letter radio station call letters can be made a. if the first letter must be Upper F comma Upper Z comma Upper T comma or Upper M and no letter may be repeated? b. if repeats are allowed (but the first letter is Upper F comma Upper Z comma Upper T comma or Upper M)? c. How many of the 6-letter radio station call letters (starting with Upper F comma Upper Z comma Upper T comma or Upper M) have no repeats and end with the letter Upper S? a. If the first letter must be Upper F comma Upper Z comma Upper T comma or Upper M, and all the letters in the radio station call letters must be different, then there are _____ 6-letter radio station call letters. b. If the first letter must be Upper F comma Upper Z comma Upper T comma or Upper M, and letters can be repeated, then there are _____ radio station call letters. c. If the first letter must be Upper F comma Upper Z comma Upper T comma or Upper M, and the last letter must be Upper S and all the letters in the radio station call letters must be different, then there are _____ 6 -letter words.
a. 25502400 b. 47525504 c. 1020096
Michael has 7 green, 3 red and 9 blue M&Ms. If he selects 5 M&Ms: a. In how many different ways can he select at least 2 blue M&Ms? b. In how many ways can he select exactly one blue and one red M&M? c. In how many ways can he get exactly 4 of the same color?
a. 9486 Solution 11628 - {[c(9, 1) * c(10, 4)] + [c(9, 0) * c(10, 5)]} = 9486 b. 945 Solution c(9, 1) * c(3, 1) * c(7, 3) = 945 c. 1680 Solution [c(7, 4) * c(12, 1)] + [c(9, 4) * c(10, 1)] = 1680