Quiz
Mathematics
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Questions in this quiz (105)
1 How many chords can be drawn through 8 points on a circle?
- A12
- B42
- C64
- D28
- E32
2How many three digit numbers can be formed from the digits: 1, 2, 3, 4, 5 ?
- A625
- B100
- C10
- D125
- E265
3How many three digit numbers can be formed from the digits: 1, 2, 3, 4, 5 and 6, if each digit
can be used once?- A120
- B100
- C10
- D125
- E265
4How many three digit numbers can be formed with the digits: 0, 1, 2, 3, 4, 5 ?
- A125
- B100
- C180
- D45
- E260
5In how many ways is it possible to choose a white square and a black square on a chess board
(8×8) so that the squares must not lie in the same row or column?- A800
- B768
- C512
- D1024
- E688
6A coin is tossed twice. Find the probability that the coin lands on “tails” in both times.
- A1/2
- B3/4
- C1
- D1/4
- E1/8
7 A coin is tossed twice. Find the probability that the coin lands on “tails” at least once.
- A1/2
- B3/4
- C1
- D1/4
- E1/8
8Two dice are tossed. Find the probability that the product of aces does not exceed 5
- A0.5
- B5/6
- C1/6
- D5/36
- E5/18
9Two dice are tossed. Find the probability that the sum of aces does not exceed 5
- A0.5
- B5/6
- C1/6
- D1/3
- E5/18
10There are 5 white, 10 black, 15 blue and 20 red balls in an urn. One ball is randomly extracted.
Find the probability that the extracted ball is blue or red- A0.5
- B0.7
- C1/7
- D0.3
- E3/5
11There are 5 white, 10 black, 15 blue and 20 red balls in an urn. One ball is randomly extracted.
Find the probability that the extracted ball isn’t black.- A0.8
- B0.5
- C4/7
- D1/3
- E0.6
12A 5 digit PIN number can begin with any digit (except zero) and the remaining digits have no
restriction. If repeated digits are allowed, the probability of the PIN code beginning with a 7 and
ending with an 8 is- A1/10
- B2/5
- C1/100
- D1/90
- E7/9
13Seven people are randomly selected from a group of 6 men and 5 women to form a committee.
The probability exactly 5 males are in the committee is- A5/14
- B1/7
- C2/15
- D9/14
- E2/11
14Five balls are drawn without replacement from a bag containing 3 metal balls and 5 glass balls.
The probability at least 3 glass balls are drawn is- A23/28
- B14/29
- C15/29
- D25/28
- E11/14
15A bookcase contains 6 different math books and 12 different physics books. If a student
randomly selects two of these books, the probability they are both math books or both physics- A1/3
- B5/18
- C9/17
- D2/9
- E5/17
16There are 5 white and 5 black balls in an urn. What is the probability of extracting a red ball
from the urn?- A1
- B0
- C1/2
- D1/5
- E1/3
17Seven people are randomly selected from a group of 6 men and 5 women to form a committee.
The probability exactly 5 males are in the committee is- A5/14
- B1/7
- C2/15
- D9/14
- E2/11
18Five balls are drawn without replacement from a bag containing 3 metal balls and 5 glass balls.
The probability at least 3 glass balls are drawn is- A23/28
- B14/29
- C15/29
- D25/28
- E11/14
19A bookcase contains 6 different math books and 12 different physics books. If a student
randomly selects two of these books, the probability they are both math books or both physics
books is- A1/3
- B5/18
- C9/17
- D2/9
- E5/17
20There are 5 white and 5 black balls in an urn. What is the probability of extracting a red ball
from the urn?- A1
- B0
- C1/2
- D1/5
- E1/3
21An urn contains 5 red, 3 white and 4 blue balls. What is the probability of extracting a black
ball from the urn?- A3/12
- B0
- C1
- D5/12
- E1/3
22Four coins are tossed. What is the probability that at least one of the coins lands on “heads”?
- A1/16
- B7/8
- C1/4
- D15/16
- E3/4
23Three shooters shoot in a target. The probability of hit in the target at one shot for the 1st shooter is 0,5; for the 2nd– 0,8 and for the 3rd– 0,9. Find the probability that at least one of the shooters will not hit in the target.
- A0.36
- B0.64
- C0.72
- D0.18
- E0.5
24Two dice are tossed. Find the probability that the sum of aces is divided on 7.
- A1/7
- B1/4
- C7/36
- D1/6
- E0.5
25Two dice are tossed. Find the probability that the sum of aces is divided on 11
- A1/18
- B1/4
- C5/36
- D1/6
- E0
26Two dice are tossed. Find the probability that the sum of aces is divided on 13.
- A1/18
- B1/4
- C5/36
- D1/6
- E0
27The events A and B are independent,
P(A') = 0,2; P(B) =0,6 Find P(A * B').- A0.12
- B0.24
- C0.32
- D0.48
- E0.16
28Two shots are made in a target by two guns. The probability of hit from the first gun is 0,9,from the second gun – 0,7. Find the probability of only one hit in the target
- A0.34
- B0.18
- C0.63
- D0.72
- E0.68
29An urn contains 4 white and 6 black balls. Two balls are randomly extracted from the urn.
What is the probability that both balls are black?- A2/5
- B7/12
- C1/3
- D3/5
- E1/12
30An urn contains 5 red, 3 white and 4 black balls. What is the probability of extracting a black ball from the urn?
- A1/3
- B0
- C0.25
- D0.5
- E5/12
31An urn contains 4 white and 6 black balls. Two balls are randomly extracted from the urn.
What is the probability that both balls are white?- A6/15
- B7/15
- C0.7
- D2/15
- E1/15
32In a batch of 5 products 2 of them have the first grade and 3 – the second grade. Two products
are randomly taken. Find the probability that both products have the second grade- A0.6
- B0.3
- C0.1
- D0.5
- E0.4
33In a batch of 5 products 2 of them have the first grade and 3 – the second grade. Two products
are randomly taken. Find the probability that they have different grades- A0.6
- B0.3
- C0.1
- D0.5
- E0.4
34Two shooters simultaneously shoot in a target. The probability of hit in the target by first
shooter is 0,7, and by the second – 0,8. Find the probability that none of shooters will hit in the
target.- A0.38
- B0.04
- C0.06
- D0.56
- E0.96
35A coin is tossed 4 times. Find the probability that the coin lands on heads only once
- A0.25
- B0.5
- C0.75
- D0.15
- E0.35
36A coin is tossed 5 times. Find the probability that the coin lands on heads 5 times
- A7/32
- B0.65
- C0.5
- D5/32
- E1/32
37A coming up seeds of wheat makes 60 %. Find the probability that two of five sown seeds will
come up- A0.563
- B0.2568
- C0.2304
- D0.7208
- E0.312
38A coming up seeds of wheat makes 60 %. Find the probability that none of four sown seeds will
come up- A0.0426
- B0.1248
- C0.463
- D0.0256
- E0.124
39A shooter makes 3 shots in a target. The probability of hit in the target at one shot is equal to
0,8. Find the probability that at least one shot will hit in the target.- A0.9
- B0.992
- C0.81
- D0.5
- E1
40During the year two firms have an opportunity independently from each other to go bankrupt
with probabilities 0,05 and 0,1. Find the probability that at the end of the year both firms will
function.- A0.64
- B0.855
- C0.45
- D0.38
- E0.256
41A card is drawn at random from an ordinary deck of 52 playing cards. What is the probability
that the card is a queen?- A4/13
- B1/52
- C0.4
- D1/13
- E0.725
42A card is drawn at random from an ordinary deck of 52 playing cards. What is the probability
that the card is a king or a spade?- A4/13
- B1/52
- C0.4
- D1/13
- E0.725
43A card is drawn at random from an ordinary deck of 52 playing cards. What is the probability
that the card is a queen or a king?- A2/13
- B1/52
- C0.4
- D1/13
- E0.725
44One bag contains 5 white and 4 black balls. Another bag contains 7 white and 9 black balls. A
ball is transferred from the first bag to the second and then a ball is drawn from second. What will
be the probability that the ball is white?- A4/9
- B8/71
- C0.35
- D5/12
- E0.23
45One bag contains 5 white and 4 black balls. Another bag contains 7 white and 9 black balls. A
ball is transferred from the first bag to the second and then a ball is drawn from second. What will
be the probability that the ball is black?- A5/9
- B8/71
- C0.35
- D85/123
- E0.23
46A factory production line is manufacturing bolts using three machines, A, B and C. Of the total
output, machine A is responsible for 25%, machine B for 35% and machine C for the rest. If it is
known from previous experience with the machines that 5% of the output from machine A is
defective, 4% from machine B and 2% from machine C. A bolt is chosen at random from the
production line and found to be defective. What is the probability that it came from machine A?- A25/69
- B49/57
- C28/69
- D25/57
- E16/69
47A factory production line is manufacturing bolts using three machines, A, B and C. Of the total
output, machine A is responsible for 25%, machine B for 35% and machine C for the rest. If it is
known from previous experience with the machines that 5% of the output from machine A is
defective, 4% from machine B and 2% from machine C. A bolt is chosen at random from the
production line and found to be defective. What is the probability that it came from machine B?- A25/69
- B49/57
- C28/69
- D25/57
- E16/69
48Machines A and B produce 10% and 90% respectively of the production of a component
intended for the motor industry. From experience, it is known that the probability that machine A
produces a defective component is 0.01 while the probability that machine B produces a defective
component is 0.05. If a component is selected at random from a day’s production and is found to be
defective, find the probability that it was made by machine A.- A0.65
- B0.02
- C0.12
- D0.35
- E0.98
49Machines A and B produce 10% and 90% respectively of the production of a component
intended for the motor industry. From experience, it is known that the probability that machine A
produces a defective component is 0.01 while the probability that machine B produces a defective
component is 0.05. If a component is selected at random from a day’s production and is found to be
defective, find the probability that it was made by machine B.- A0.65
- B0.02
- C0.12
- D0.35
- E0.98
50Five independent trials have been made in each of which the probability of occurrence of an
event A is equal to 0.2. Find the probability that the event A will appear at least 4 times.- A0.00096
- B0.00587
- C0.33458
- D0.08
- E0.07
51The mathematical expectation M(C) of a constant C is equal to
- AC
- B1
- C0
- DC^2
52The dispersion D(C) of a constant C is equal to
- AC
- B1
- C0
- DC^2
53The dispersion of the difference of two independent random variables Х and Y is equal to
- AD(X - Y) = D(X) - D(Y)
- BD(X - Y) = D(X) D(Y)
- CD(X - Y) = D(X^2)
- DD(X - Y) = D(Y^2)
- ED(X - Y) = D(X) +D(Y)
54Show one of the properties of mathematical expectation of a random variable X (C is a constant):
- AM(CX) = M(C) + M(X)
- BM(C + X) = M(X)
- CM(CX) = CM(X)
- DM(CX) = M(C) – M(X)
- EM(C + X) = M(C)
55Show one of the properties of dispersion of a random variable X (C is a constant):
- AM(CX) = M(C) + M(X)
- BM(C + X) = M(X)
- CM(CX) = CM(X)
- DM(CX) = M(C) – M(X)
- EM(C + X) = M(C)
56Show one of the properties of dispersion of a random variable X (C is a constant)
- AD(C + X) = D(C) + D(X)
- BD(C + X) = D(X)
- CD(CX) = CD(X)
- DD(C – X) = D(C) – D(X)
- ED(CX) = D(C)
57The mathematical expectation of a random variable Х is 4. Find М(3Х-7)
- A12
- B7
- C17
- D0
- E5
58The dispersion of a random variable X is 2. Find D(3Х-7)
- A-1
- B18
- C13
- D14
- E0
59The random variables X and Y are independent. Find the dispersion of the random variable Z=2X – 3Y+ 5 if it is known that D(X) = 2, D(Y) = 4.
- A49
- B-3
- C44
- D56
- E-4
60The random variables X and Y are independent. Find the dispersion of the random variable Z
= 5X – Y+ 6 if it is known that D(X) = 2, D(Y) = 0,9.- A56.9
- B27.7
- C3.45
- D49.1
- E50.9
61The random variables X and Y are independent. Find the mathematical expectation of the
random variable Z = 5X – Y+ 6 if it is known that M(X) = - 1, M(Y) =6.- A13
- B-5
- C-6
- D6
- E-4
62The law of distribution of a discrete random variable X is given by the following table:
x -2 a
p 0.7 0.3
It is known that M(X) = 0,1. Find a.- A1
- B2
- C3
- D4
- E5
63A discrete random variable X is given by the following law of distribution:
x 1 2 4
p 0.1 0.3 0.6
A discrete random variable X is given by the following law of distribution:- A3.4
- B3.1
- C2.8
- D2.4
- E0.76
64A discrete random variable X is given by the following law of distribution:
X x2 x2 x3 x4
P 0,1 0,35 p3 0,15
Find p3- A0.4
- B0.45
- C0
- D1
- E0.15
659. Find the mathematical expectation M(X) of a random variable X, knowing its law of
distribution:
x -2 0 1
p 1/ 7 3 / 7 3 / 7- A2/7
- B0
- C7
- D0.7
- E1/7
66Find the mean square deviation σ(X) of a random variable X, knowing its law of distribution:
x 0 1 3
p 0,2 0,4 0,4- A1.2
- B0.1
- C2
- D0.2
- E0.5
67A random variable X has the following law of distribution:
x 0 1 2 3
p 1/30 3/10 1/ 2 1/ 6
Find the mathematical expectation of X- A1
- B1.5
- C2
- D1.8
- E2.3
68Let a random variable X be given by the following law of distribution:
x -3 -2 0 2 3
p 0,1 0,2 0,4 0,2 0.1
Find the mathematical expectation M(X).- A2
- B0.1
- C0.2
- D0
- E1
69Let a random variable X be given by the following law of distribution:
x -3 -2 0 2 3
p 0,1 0,2 0,4 0,2 0.1
Find the mathematical expectation D(X).- A0
- B3.4
- C1
- D0.34
- E0.1
70The dispersion of the number of occurrences of an event A for n independent trials in each of
which the probability of occurrence of the event A is p, is equal to:- AD(X ) = np
- BD(X)=nq
- CD(X)=npq
71The mathematical expectation of the number of occurrences of an event A for n independent
trials in each of which the probability of occurrence of the event A is p, is equal to:- AM(X)=np
- BM(X)=nq
- CM(X)=p
- DM(X)=npq
- EM(X)=n(p+q)
72The integral function of distribution F(x) of a random variable X is defined by
- AF(x)=P(X>x)
- BF(x)=P(X<x)
- CF(x)=P(X>=x)
- DF(x)=P(X>=a)
- EF(x)=P(X=x)
73If all possible values of a random variable X belong to an interval (a, b) then the integral
function of distribution F(x) for
x > b
is equal to:- A1
- B0
- C0.5
- D-1
- E2
74If all possible values of a random variable X belong to an interval (a, b) then the integral
function of distribution F(x) for
x <= a
is equal to:- A1
- B0
- C0.5
- D-1
- E2
75If F(x) is the integral function of a random variable X then
- AF(x)>1
- BF(x)<=0
- CF(x)<0
- D0<=F(x)<=1
- EF(x)>=1
76The probability of hit of a random variable into an interval (a, b) is equal to
- AF(b)+F(a)
- BF(a)F(b)
- CF(b)-F(a)
- DF(b-a)
- EF(a)-F(b)
77An integral function of distribution F(x) is
- Adecreasing
- Bnon-decreasing
- Cperiodic
- Deven
- Eodd
78If F(x) is the integral function and f (x) is the probability density of a random variable X, then
- Af (x) =F'(x)
- Bf '(x) =F(x)
- Cf (x) =F(x)
- Df '(x) =F'(x)
- Ef (x) =F(-x)
79The graph of the density of distribution f(x) of a continuous random variable X cannot be:
- Abelow the axis Ox
- Bupper the axis Ox
- Cto the left of the axis Oy
- Dto the right of the axis Oy
80If a random variable X is uniformly distributed on the segment [a, b], then its mathematical
expectation is equal to- AM (X ) = a
- BM (X ) = (a+b)/2
- CM (X ) = a+b
- DM (X ) = (a-b)/2
- EM (X ) = b
81If a random variable X is uniformly distributed on the segment [a, b], then its dispersion is
equal to- AD(X ) = b
- BD(X ) = (b-a)^2/12
- CD(X ) = (b+a)/2
- DD(X ) = (b-a)/2
- ED(X ) = (b-a/12)^2
82A discrete variation series of a sample is given:
n 4 16 5
x 2 1 4
Find the volume of the
variation series- A3
- B25
- C16
- D4
- E1
83The sum of frequencies of all variants of a sample is equal to:
- AThe volume of a sample
- BThe sample dispersion
- C0
- Do The sample mean
- E1
84The sum of relative frequencies of all variants of a sample is equal to:
- AThe sample dispersion
- B1
- CThe sample mean
- DThe volume sample
- E0
85A discrete variation series of a sample is given:
x 4 16 5
n 2 1 4
Find the median of the
variation series.- A5
- B16
- C4
- D-2
- E1
86A discrete variation series of a sample is given:
x 4 16 5
n 2 1 4
Find the mode of the
variation series.- A3
- B25
- C16
- D4
- E1
87A discrete variation series of a sample is given:
4 16 5
2 1 4
Find the sample mean
x .- A1,12
- B2,08
- C16
- D28
- E0
88A discrete variation series of a sample is given:
4 16 5
2 1 4
Find the sample
dispersion
2
s .- A1,2234
- B3,2256
- C4
- D0,82
- E0
89A discrete variation series of a sample is given:
20 50 18 12
2 0 1 5
Find the volume of
the variation series.- A15
- B50
- C200
- D40
- E100
90A discrete variation series of a sample is given:
20 50 18 12
2 0 1 5
Find the median
of the variation series- A50
- B1
- C0,5
- D15
- E0
91A discrete variation series of a sample is given:
20 50 18 12
2 0 1 5
Find the mode of
the variation series- A3
- B7,5
- C16
- D0
- E1
92A discrete variation series of a sample is given:
20 50 18 12
2 0 1 5
Find the sample
mean
x .- A15
- B5
- C16
- D38
- E0,38
93A discrete variation series of a sample is given:
20 50 18 12
2 0 1 5
Find the sample
dispersion
2- A1,2234
- B3,8356
- C4
- D0
- E0,8447
94Find the mode of the following sample: {6, 6, 7, 10, 12, 12, 12}
- A11
- B10
- C6
- D5
- E12
95. Find the mode of the following sample: {1,1,1,2,3,3,3,7,8,8,8,8}
- A1
- B2
- C3
- D7
- E8
96 Find the median of the following sample: {1,1,1,2,3,3,3,7,8,8,8,8}
- A8
- B1
- C3
- D2
- E5
97Given the sample: {1,1,1,2,3,3,3,7,8,8,8,8}. Find the sample mean
- A8
- B45/11
- C3
- D4/13
- E53/12
98Find the median of the following sample: {10, 10, 10, 15, 15, 20, 20}
- A15.5
- B10
- C25
- D15
- E20
99Find the mode of the following sample: {10, 10, 10, 15, 15, 20, 20}.
- A15,5
- B10
- C25
- D15
- E20
100Given the sample: {10, 10, 10, 15, 15, 20, 20}. Find the sample mean
- A15,5
- B10
- C15
- D100/7
- E20
101Results of sampling inspections of one-day profits of city shops are given: {5, 5, 10, 14, 18,
20, 25}. Find the median.- A30
- B10
- C25
- D16
- E148
102How will the sample mean change if all variants are increased in 5 times?
- Awill increase in 5 times
- Bwill decrease in 5 times
- Cwill increase in 25 times
- Dwill decrease in 25 times
103How will the sample dispersion change if all variants are increased in 5 times?
- Awill increase in 5 times
- Bwill decrease in 5 times
- Cwill increase in 25 times
- Dwill idecrease in 25 times
104How will the sample dispersion change if all variants are increased on 6?
- Awill decrease on 36
- Bwill decrease on 6
- Cwill increase on 36
- Dwill increase on 6
- Enot change
105How will the sample mean change if all variants are increased on 6?
- Awill decrease on 36
- Bwill decrease on 6
- Cwill increase on 36
- Dwill increase on 6
- Enot change
Information
- Description
- Quiz on Mathematics , created by Меруерт Бекен on 25/12/2019.
- Author
- Меруерт Бекен
- Language
- English
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