Free Printable twims

1.

The number of all possible permutations

a)

𝑃𝑛 = 𝑛!

b)

𝑃𝑛 = 𝑛! 𝑚!

c)

𝑃𝑛 = 𝑛! 𝑚!/(𝑛−𝑚)!

d)

𝑃𝑛 = (𝑛 + 1)!

2.

How many two-place numbers can be made of the digits 1, 4, 5 and 7 if each digit is included into the image of a number only once?

a)

24

b)

12

c)

16

d)

3

3.

The number of all possible allocations

a)

$A_n^m=\frac{n!}{\left(n-m\right)!}$

b)

$A_n^m=\frac{n!}{m!\left(n-m\right)!}$

c)

$A_n^m=n-m!$

d)

$A_n^m=m-n!$

4.

The number of all possible combinations

a)

$C_n^m=\frac{n!}{m!\left(n-m\right)!}$

b)

$C_n^m=\frac{n!}{\left(n-m\right)!}$

c)

$C_n^m=\frac{m!}{n!}$

d)

$C_n^m=n!$

5.

How many ways are there to choose 2 details from a box containing 9 details?

a)

12

b)

4

c)

22

d)

36

6.

The numbers of allocations, permutations and combinations are connected by the equality

a)

$A_n^m=P_mC_n^m$

b)

$A_n^m=P_nC_n^m$

c)

$A_n^m=P_m$

d)

$A_n^m=P_mC_m^n$

7.

If some object A can be chosen from the set of objects by m ways, and another object B can be chosen by n ways, then we can choose either A or B by … ways.

a)

m-n

b)

n!

c)

m+n

d)

$C_n^m$

8.

Events are equally possible if …

a)

none of them will necessarily happen as a result of a trial

b)

there is reason to consider that none of them is more possible (probable) than other

c)

there is reason to consider that one of them is more possible (probable) than other

d)

at least one of them will necessarily happen as a result of a trial

9.

The probability of the event A is determined by the formula

a)

𝑃(𝐴) = |Ω| /|𝐴| , where is the space of elementary outcomes

b)

𝑃(𝐴|𝐵) = |𝐴| /|𝐵| , where is the space of elementary outcomes

c)

𝑃(𝐴) = | 𝐴|/ |Ω| , where is the space of elementary outcomes

d)

𝑃(𝐴) = 𝜆𝑚 𝑚! 𝑒 −𝜆 , where 𝜆 is the space of elementary outcomes

10.

The probability of a reliable event is equal to

a)

0

b)

1

c)

1/3

d)

1/5

11.

. The probability of an impossible event is equal to

a)

1/5

b)

1

c)

1/3

d)

0

12.

The probability of a random event is

a)

the positive number between 0 and ½

b)

the positive number between 0 and 1

c)

the positive number between 0 and 1/3

d)

the positive number between 0 and 1/5

13.

The relative frequency of the event A is defined by the formula:

a)

𝑊(𝐴) = 𝑚/ 𝑛 , where m is the number of appearances of the event, n is the total number of trials.

b)

𝑊(𝐴) = 𝑚/ 𝑛 , where n is the number of appearances of the event, m+1 is the total number of trials

c)

𝑊(𝐴) = 𝑚 /𝑛 , where m+1 is the number of appearances of the event, n is the total number of trials.

d)

𝑊(𝐴) = 𝑚+1/ 𝑛 , where m is the number of appearances of the event, n is the total number of trials.

14.

There are 100 identical details (and 20 of them are painted) in a box. Find the probability that the first randomly taken detail will be painted.

a)

1/20

b)

1/5

c)

1/10

d)

1/9

15.

A die is tossed. Find the probability that an even number of aces will appear.

a)

½

b)

1/3

c)

1

d)

1/5

16.

Participants of a toss-up pull a ticket with numbers from 1 up to 30 from a box. Find the probability that the number of the first randomly taken ticket contains the digit 2.

a)

1/30

b)

1/3

c)

½

d)

2/5

17.

In a batch of 8 details the quality department has found out 3 non-standard details. What is the relative frequency of appearance of non-standard details equal to?

a)

½

b)

1

c)

3/11

d)

3/8

18.

At shooting by a rifle the relative frequency of hit in a target has appeared equal to 0,4. Find the number of hits if 20 shots were made.

a)

8

b)

3

c)

20

d)

1

19.

Two dice are tossed. Find the probability that different number of aces will appear on dices

a)

1/6

b)

5/6

c)

½

d)

1/3

20.

Two dice are tossed. Find the probability that the sum of aces will exceed 10

a)

1/12

b)

5/12

c)

5/18

d)

1/18

21.

An urn contains 15 balls: 4 white, 6 black and 5 red. Find the probability that a randomly taken ball will be red or white.

a)

3/7

b)

4/15

c)

3/5

d)

6/15

e)

1

22.

12 seeds have germinated of 60 planted seeds. Find the relative frequency of germination of seeds.

a)

1/5

b)

4/5

c)

1/60

d)

1/12

23.

A point C is randomly appeared in a segment AB of the length 5. Determine the probability that the distance between C and B doesn’t exceed 1.

a)

2/5

b)

1/5

c)

4/5

d)

0

twims

Total questions: 23

Worksheet time: 12mins

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