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Mat I part
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Questions in this quiz (40)
11. Bob has three bookshelves in his office and 15 books (5 are math books, 10 are novels). If each
shelf holds exactly five books and books are placed randomly on the shelves (all orderings are
equally likely), how many ways can 15 books be arranged on a bookshelves?- A15!/10!
- B15! / ( 10! * 5! )
- C15! / (5!)^3
- D15! / (3)^3
- E( 15! * 3! ) / ( 5! * 10! )
22. A class in probability theory consists of 2 men and 8 women. They passed exam, took their
score. Assume that no two students took the same score. How many different scores are
possible?- A2! * 8!
- B10!
- C10! / 2!
- D10! / 2! * 8!
- E10! / (2!)^2
33. A class in probability theory consists of 6 men and 4 women. They passed exam, took their
score. Assume that no two students took the same score. How many different scores are
possible?- A6! * 4!
- B10!
- C10! / 2!
- D10! / 4! * 6!
- E10! / 2!^2
44. Ms. Jones has 10 books that she is going to put on her bookshelf. Of these, 4 are math books, 3
are chemistry books, 2 are history books, and 1 is a language book. Ms. Jones wants to
arrange her books so that all the books dealing with the same subject are together on the shelf.
How many different arrangements are possible?- A288
- B6912
- C12600
- D525
- E3456
55. How many different signals, each consisting of 9 flags hung in a line, can be made from a set of
4 white flags, 3 red flags, and 2 blue flags if all flags of the same color are identical?- A288
- B6912
- C1260
- D525
- E3456
66. From a group of 5 women and 7 men, how many different committees consisting of 2 women
and 3 men can be formed, if 2 of the men are refuse to serve on the committee together?- A350
- B300
- C4200
- D500
- E220
77. A student answers to 10 questions in an examination. How many choices if she answered at
7 questions?- A120
- B176
- C45
- D10
- E220
88. A student answers to 10 questions in an examination. How many choices if she answered at
least 7 questions?- A120
- B176
- C45
- D10
- E220
99. An urn contains 30 balls, of which 10 are red and the other 20 blue. Suppose you take out 8
balls from this urn, without replacement. In how many ways among chosen 8 balls in this
sample exactly 3 are red and 5 are blue?- A5852925
- B1860480
- C3720960
- D2480640
- E4961280
1010. A bag contains six Scrabble tiles with the letters A-D-M-N-O-R. You reach into the bag and
take out tiles one at a time. After you pick a tile from the bag, write down that letter and then
return the tile to the bag. How many possible words can be formed?- A720
- B6
- C46656
- D120
- E10240
1111. A police department in a small city consists of 10 officers. If the department policy is to have 5
of the officers patrolling the streets, 2 of the officers working full time at the station, and 3 of
the officers on reserve at the station, how many different divisions of the 10 officers into the 3
groups are possible?- A350
- B2520
- C4200
- D300
- E220
1212. Joel has an MP3 player called the Jumble. The Jumble randomly selects a song for the user to
listen to. Joel's Jumble has 2 classical songs, 13 rock songs and 5 rap songs on it. What is the
probability that the selected song is classical song or rap song?- A0,9
- B13/20
- C0,35
- D7
- E0,7
1313. A chess tournament has 10 competitors, of which 4 are Russian, 3 are from the USA, 2 are
from Great Britain, and 1 is from Brazil. If the tournament result lists just the nationalities of
the players in the order in which they placed, how many outcomes are possible?- A288
- B6912
- C12600
- D525
- E3456
1414. An urn contains 10 balls: 4 red and 6 blue. A second urn contains 16 red balls and an unknown
number of blue balls. A single ball is drawn from each urn. The probability that both balls are
the same color is 0.44. Calculate the number of blue balls in the second urn.- A64
- B16
- C4
- D32
- E8
1515. An urn contains 10 balls: 4 red and 6 blue. A second urn contains 16 red balls and an unknown
number of blue balls. A single ball is drawn from each urn. The probability that both balls are
the different color is 0.44. Calculate the number of blue balls in the second urn.- A4
- B16
- C64
- D32
- E8
1616. License plates in Minnesota are issued with three letters from A to Z followed by three digits
from 0 to 9. If each license plate is equally likely, what is the probability that a random license
plate starts with G-Z-N?- A10^3 / 26^3
- B10^3
- C1 / 26^3
- D1 / 10^3
- E26^3
1717. A business man has 4 dress shirts and 7 ties. How many different shirt/tie outfits can he create?
- A4
- B7
- C28
- D11
- E8
1818. Mark is taking four final exams next week. His studying was erratic and all scores A, B, C, D,
and F are equally likely for each exam. What is the probability that Mark will get at least one
A?- A0.3264
- B0.8712
- C0.5904
- D0.6124
- E0.9122
1919. Mark is taking four final exams next week. His studying was erratic and all scores A, B, C, D,
and F are equally likely for each exam. What is the probability that Mark will get at least one
B?- A0.3264
- B0.8712
- C0.5904
- D0.6124
- E0.9122
2020. I tell students in my class that, although I use an average to calculate their course grades, I do
weigh the final exam grade more heavily. I assure them that if they can perform well on my
final, then even if they performed poorly on the other exams, they must have learned the
material. For three semesters I kept track of how people did on the final and how they did in the
course. Using the given data, answer the following question.------------photo------------Total number of
students 321. What is the probability that a student, taken at random from my class, would
have failed the course, given that they failed the final?
- A0.39
- B0.72
- C0.61
- D0.44
- E0.58
2121. I tell students in my class that, although I use an average to calculate their course grades, I do
weigh the final exam grade more heavily. I assure them that if they can perform well on my
final, then even if they performed poorly on the other exams, they must have learned the
material. For three semesters I kept track of how people did on the final and how they did in the
course. Using the given data, answer the following question.-------photo------- Total number of
students 321. What is the probability that a student, taken at random from my class, would
have passed the course, given that they failed the final?
- A0.39
- B0.72
- C0.61
- D0.44
- E0.58
2222. I tell students in my class that, although I use an average to calculate their course grades, I do
weigh the final exam grade more heavily. I assure them that if they can perform well on my
final, then even if they performed poorly on the other exams, they must have learned the
material. For three semesters I kept track of how people did on the final and how they did in the
course. Using the given data, answer the following question.--------photo--------Total number of
students 321. What is the probability that a student, taken at random from my class, would
have passed the course, given that they passed the final?- A0.39
- B0.72
- C0.81
- D0.44
- E0.61
2323. I tell students in my class that, although I use an average to calculate their course grades, I do
weigh the final exam grade more heavily. I assure them that if they can perform well on my
final, then even if they performed poorly on the other exams, they must have learned the
material. For three semesters I kept track of how people did on the final and how they did in the
course. Using the given data, answer the following question.---------photoo--------Total number of
students 321. What is the probability that a student, taken at random from my class, would
have failed the course, given that they passed the final?- A0.19
- B0.39
- C0.81
- D0.44
- E0.61
2424. Insurance predictions for probability of auto accident.
Table gives an insurance company’s
prediction for the likelihood that a person in a particular age group will have an auto accident
-----photo -----------during the next year. The company’s policyholders are 20% under the age of 25, 30% between
25 and 39, and 50% over the age of 40. What is the probability that a random policyholder will
have an auto accident next year?
- A0.145
- B0.041
- C0.367
- D0.512
- E0.845
2525. At a certain university, 4% of men are over 6 feet tall and 1% of women are over 6 feet tall. The
total student population is divided in the ratio 3:2 in favour of women (the number of women :
the number of men). What is the probability that the randomly selected student is over 6 feet
tall?- A0.05
- B0.022
- C0.14
- D0.028
- E0.11
2626. You enter a chess tournament where your probability of winning a game is 0.3 against half the
players, 0.4 against a quarter of the players, and 0.5 against the remaining quarter of the
players. You play a game against a randomly chosen opponent. What is the probability of
winning?- A1.2
- B0.375
- C0.12
- D0.028
- E0.648
2727. If a person has the disease, the test will detect it with probability 0.95. Also, if the person does
not have the disease, the test will report that they do not have it with the same probability 0.95.
In addition, it is known from previous data that only 1% of the population has this particular
disease. What is the probability that a particular person chosen at random will be tested
positive?- A0.043
- B0.059
- C0.01
- D0.95
- E1.2
2828. Suppose that you have two bags with white and dark chocolates. Bag 1 has two white chocolates
and six dark chocolates. Bag 2 has four white chocolates and two dark chocolates. You choose
one bag at random, both being equally likely, and you grab one from the chosen bag. Let A be
the event that you grab one white chocolate. Find P(A)- A11/12
- B11/24
- C13/32
- D1/3
- E1/2
2929. Amy has two bags of candy. The first bag contains two packs of M&Ms and three packs of
Gummi Bears. The second bag contains four packs of M&Ms and two packs of Gummi Bears.
Amy chooses a bag uniformly at random and then picks a pack of candy. What is the
probability that the pack chosen is Gummi Bears?- A11/12
- B7/15
- C14/15
- D1/3
- E1/2
3030. Amy has three bags of candy. The first bag contains one pack of M&Ms and two packs of
Gummi Bears. The second bag contains four packs of M&Ms and two packs of Gummi Bears.
The third bag contains five packs of M&Ms and three packs of Gummi Bears. Amy chooses a
bag uniformly at random and then picks a pack of candy. What is the probability that the pack
chosen is M&Ms?- A11/12
- B13/24
- C2/7
- D5/8
- E1/2
3131. Amy has two bags of candy. The first bag contains two packs of M&Ms and three packs of
Gummi Bears. The second bag contains four packs of M&Ms and two packs of Gummi Bears.
Amy chooses the first bag with the probability 0.3 and the second – 0.7. Amy chooses a bag at
random and then picks a pack of candy. What is the probability that the pack chosen is M&Ms?- A13/24
- B44/75
- C7/15
- D5/8
- E1/2
32Tile values in Scrabble. In the game
of Scrabble, there are 100 letters tiles with the distribution of point values given in Table. Let X
be the point value of a random Scrabble tile. What is the mathematical expectation of X?
- A187
- B1.87
- C18.7
- D0.187
- E19
3333. Tile values in Scrabble. In the game of Scrabble,
there are 100 letters tiles with the distribution of point values given in Table. Let X be the point
value of a random Scrabble tile. What is the mathematical expectation of X^2 ?
- A1.87
- B4.71
- C3.26
- D5.2
- E9.1
3434. A fair six-sided die is tossed. You win $2 if the result is a «1», you win $1 if the result is a «6»,
but otherwise you lose $1. What is the dispersion of X?- A1.74
- B1.47
- C-0.17
- D1.5
- E2.12
3535. A fair six-sided die is tossed. You win $2 if the result is a «1», you win $1 if the result is a «6» or
«3», but otherwise you lose $1. What is the dispersion of X?- A1.74
- B1.47
- C-0.17
- D1.5
- E2.12
3636. Which of the following is a discrete random variable?
- AThe time of waiting a train.
- BThe number of boys in family having 4 children.
- CA time of repair of TVs.
- DThe velocity in any direction of a molecule in gas.
- EThe height of a man.
3737. Which of the following is a discrete random variable?
- AThe time of waiting a train.
- BThe number of people in a community living to 100 years of age.
- CThe mistake of a rounding off of a number up to the whole number.
- DThe velocity in any direction of a molecule in gas.
- EThe amount of time (starting from now) until an earthquake occurs.
3838. Two independent random variables X and Y are given by the following tables of distribution:
Find the mathematical expectation
of X+Y?
- A2.3
- B3.8
- C1
- D5.2
- E2.4
39Two independent random variables X and Y are given by the following tables of distribution:
Find the mean square deviation of
X+Y?- A2.13
- B1.296
- C1.457
- D1.795
- E2.4
4040. Two independent random variables X and Y are given by the following tables of distribution:
Find the mathematical expectation
of XY?- A-3.8
- B-3.36
- C-1.4
- D-4.26
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- Quiz on Mat I part, created by hoffa HOFFMAN on 27/12/2019.
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- hoffa HOFFMAN
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- Created on 27 Dec 2019 · updated on 28 Dec 2019
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