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Math 1 1-50
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Questions in this quiz (50)
11. The number of all possible permutations
- AP_n=n!
- BP_n=n!/m!
- CP_n=n!/m!(n-m)!
- DP_n=n!/(n-m)!
- EP_n=(n+1)!
22. 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?
- Ao 24
- Bo 12
- Co 16
- Do 3
- Eo 2
33. The number of all possible allocations
- AA_n^m=n!/(n-m)!
- BA_n^m=n!/m!(n-m)!
- CA_n^m=n-m!
- DA_n^m=m-n!
- EA_n^m=1
44. The number of all possible combinations
- AC_n^m=n!/m!(n-m)!
- BC_n^m=n!/(n-m)!
- CC_n^m=m!/n!
- DC_n^m=n!/m!
- EC_n^m=n!
55. How many ways are there to choose 2 details from a box containing 9 details?
- Ao 12
- Bo 4
- Co 22
- Do 11
- Eo 36
66. 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.
- Ao m+n
- Bo m-n
- Co n-m
- Do n!
- Eo C_n^m
77. Events are equally possible if …
- Ao none of them will necessarily happen as a result of a trial
- Bo there is reason to consider that none of them is more possible (probable) than other
- Co there is reason to consider that one of them is more possible (probable) than other
- Do at least one of them will necessarily happen as a result of a trial
- Eo one of them will necessarily happen as a result of a trial
88. The probability of the event A is determined by the formula
- AP(A)=(|Ω|)/(|A|), where Ω is the space of elementary outcomes
- BP(A│B)=(|A|)/(|B|), where Ω is the space of elementary outcomes
- CP(A)=| A|/(|Ω|), where Ω is the space of elementary outcomes
- DP(A)=λ^m/m! e^(-λ), where λ is the space of elementary outcomes
- EP(B│A)=λ^m/m!, where Ω is the space of elementary outcomes
99. The probability of a reliable event is equal to …
- Ao 1
- Bo 0
- Co ½
- Do 1/3
- Eo 1/5
1010. The probability of an impossible event is equal to …
- Ao 0
- Bo 1
- Co ½
- Do 1/3
- Eo 1/5
1111. The probability of a random event is …
- Ao the positive number between 0 and 1
- Bo the positive number between 0 and ½
- Co the positive number between 0 and 10
- Do the positive number between 0 and 1/3
- Eo the positive number between 0 and 1/5
1212. 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.
- Ao 1/20
- Bo 1/5
- Co ½
- Do 1/10
- Eo 1/9
1313. A die is tossed. Find the probability that an even number of aces will appear.
- Ao ½
- Bo 1
- Co 0
- Do 1/5
- Eo 1/9
1414. 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.
- Ao 1/30
- Bo 1/3
- Co ½
- Do 2/5
- Eo 1/5
1515. In a batch of 8 details the quality department has found out 3 non-standard details. What is the probability of appearance of non-standard details equal to?
- Ao ½
- Bo 1
- Co 3/11
- Do 3/8
- Eo 3/5
1616. 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.
- Ao 8
- Bo 3
- Co 20
- Do 1
- Eo 6
1717. Two dice are tossed. Find the probability that different number of aces will appear on dices
- Ao 1/6
- Bo 5/6
- Co ½
- Do 1/3
- Eo 1
1818. Two dice are tossed. Find the probability that the sum of aces will exceed 10.
- Ao 1/12
- Bo 5/12
- Co 5/18
- Do 1/18
- Eo 0
1919. 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.
- Ao 3/7
- Bo 4/15
- Co 3/5
- Do 6/15
- Eo 1
2020. 12 seeds have germinated of 60 planted seeds. Find the relative frequency of germination of seeds.
- Ao 1/5
- Bo 4/5
- Co 1/60
- Do 1/12
- Eo 1
2121. A coin is tossed twice. Find the probability that the coin lands on tails in both times.
- Ao 1/4
- Bo 3/4
- Co 1/3
- Do ½
- Eo 0
2222. There are 200 details in a box. It is known that 150 of them are details of the first kind, 10 – the second kind, and the rest – the third kind. How many ways of extracting a detail of the first or the third kind from the box are there?
- Ao 190
- Bo 10
- Co 40
- Do 200
- Eo 150
2323. If an object A can be chosen from the set of objects by m ways and after every such choice an object B can be chosen by n ways then the pair of the objects (A, B) in this order can be chosen by ... ways.
- Ao mn
- Bo m+n
- Co n-m
- Do n!
- Eo N
2424. 5 of 20 students have sport categories. What is the probability that 3 randomly chosen students have sport categories?
- Ao 1/114
- Bo 3/5
- Co 1/10
- Do 1/57
- Eo 1/1218
2525. A box contains 5 red, 6 green and 4 blue pencils. 3 pencils are randomly extracted from the box. Find the probability that all the extracted pencils are different color.
- Ao 4/19
- Bo 15/91
- Co 24/91
- Do 3/19
- Eo 3/91
2626. It has been sold 12 of 15 refrigerators of three marks available in quantities of 5, 7 and 3 units in a shop. Assuming that the probability to be sold for a refrigerator of each mark is the same, find the probability that refrigerators of one mark have been unsold.
- Ao 0,101
- Bo 0,016
- Co 0,984
- Do 0,53
- Eo 0,8
2727. The probability of appearance of any of two incompatible events is equal to:
- AP(A+B)=P(A)+P(B)
- BP(A+B)=P(A)-P(B)
- CP(A+B)=P(A)P(B)
- DP(AB)=P(A)+P(B)
- EP(A)=P(A+B)
2828. There are 20 balls in an urn: 3 red, 2 blue and 15 white. Find the probability of appearance of a color (red or blue) ball.
- Ao 1/4
- Bo 1
- Co 3/4
- Do 1/20
- Eo 1/15
2929. A shooter shoots in a target subdivided into three areas. The probability of hit in the first area is 0,5 and in the second – 0,3. Find the probability that the shooter will hit at one shot either in the second area or in the third area.
- Ao 0,5
- Bo 0,9
- Co 1
- Do 0,7
- Eo 0,8
3030. The sum of the probabilities of events A1, A2,…, An which form a sample space is equal to …
- A• 1
- Bo 0
- Co ½
- Do 1/5
- Eo 1/3
3131. A consulting point of an institute receives packages with control works from the cities A, B and С. The probability of receiving a package from the city A is equal 0,2; from the city B – 0,2. Find the probability that next package will be received from the city С.
- Ao 0,5
- Bo 0,9
- Co 0,6
- Do 0,8
- Eo 1
3232. Two uniquely possible events forming a complete group are …
- Ao Opposite
- Bo Same
- Co Identically distributed
- Do Sample
- Eo Density function
3333. The probability that a day will be rainy is p = 0,75. Find the probability that a day will be clear.
- Ao 0,25
- Bo 0,3
- Co 0,15
- Do 0,75
- Eo 1
3434. The conditional probability of an event A with the condition that an event B has already happened is equal to:
- AP(A|B)=P(AB)/P(B)
- BP(A|B)=(P(AB))/(P(A))
- CP(A|B)=P(A)/P(B)
- DP(A|B)=P(B)/P(A)
- EP(A|B)=(P(B))/(P(AB))
3535. There are 4 conic and 8 elliptic cylinders at a collector. The collector has taken one cylinder, and then he has taken the second cylinder. Find the conditional probability that the second taken cylinder is elliptic given that the first was conic.
- Ao 8/11
- Bo 1/4
- Co 8/33
- Do 1/2
- Eo 2/3
3636. There are 4 white, 5 black and 6 blue balls in an urn. Each trial consists in extracting at random one ball without replacement. Find the probability that a white ball will appear at the first trial (the event A), a black ball will appear at the second trial (the event B), and a blue ball will appear at the third trial (the event C).
- Ao 1/22
- Bo 4/91
- Co 1/8
- Do 8/225
- Eo ½
3737. The events A, B, C and D form a complete group. The probabilities of the events are those: P(A) = 0,1; P(B) = 0,49; P(C) = 0,3. What is the probability of the event D equal to?
- Ao 0,11
- Bo 0,5
- Co 0,2
- Do 0,4
- Eo 0,1
3838. For independent events theorem of multiplication has the following form:
- AP(AB)=P(A)P(B)
- BP(AB)=P(A)+P(B)
- CP(AB)=(P(A))/P(B)
- DP(AB)=P(A)-P(B)
- EP(AB)=1
3939. Find the probability of joint hit in a target by two guns if the probability of hit in the target by the first gun (the event A) is equal to 0,3; and by the second gun (the event B) – 0,5.
- Ao 0,35
- Bo 0,15
- Co 0,2
- Do 0,8
- Eo 0,5
4040. There are 3 flat-printing machines at typography. For each machine the probability that it works at the present time is equal to 0,6. Find the probability that at least one machine works at the present time.
- Ao 0,9714
- Bo 0,256
- Co 0,36
- Do 0,784
- Eo 0,936
4141. Three students pass an exam. The probability that the exam will be passed on "excellent" by the first student is equal to 0,5; by the second – 0,2; and by the third – 0,8. What is the probability that the exam will be passed on "excellent" by only one student?
- Ao 0,42
- Bo 0,48
- Co 0,92
- Do 0,28
- Eo 0,99
4242. Three students pass an exam. The probability that the exam will be passed on "excellent" by the first student is equal to 0,5; by the second – 0,3; and by the third – 0,7. What is the probability that the exam will be passed on "excellent" by exactly two students?
- Ao 0,464
- Bo 0,395
- Co 0,12
- Do 0,192
- Eo 0,48
4343. Three students pass an exam. The probability that the exam will be passed on "excellent" by the first student is equal to 0,3; by the second – 0,7; and by the third – 0,8. What is the probability that the exam will be passed on "excellent" by at least one student?
- Ao 0,958
- Bo 0,93
- Co 0,465
- Do 0,15
- Eo 0,848
4444. Three students pass an exam. The probability that the exam will be passed on "excellent" by the first student is equal to 0,3; by the second – 0,7; and by the third – 0,8. What is the probability that the exam will be passed on "excellent" by neither of the students?
- Ao 0,042
- Bo 0,95
- Co 0,46
- Do 0,07
- Eo 0,84
4545. Three buyers went to a shop. The probability that each buyer makes purchases is equal to 0,8. Find the probability that two of them will make purchases.
- Ao 0,384
- Bo 0,7
- Co 0,189
- Do 0,96
- Eo 0,904
4646. Four buyers went in a shop. The probability that each buyer makes purchases is equal to 0,5. Find the probability that three of them will make purchases.
- Ao 0,25
- Bo 0,096
- Co 0,95
- Do 0,125
- Eo 0,712
4747. Four buyers went in a shop. The probability that each buyer makes purchases is equal to 0,8. Find the probability that only one of them will make purchases.
- A• 0,0256
- Bo 0,568
- Co 0,0441
- Do 0,064
- Eo 0,144
4848. There are 5 details made by the factory № 1 and 15 details of the factory № 2 at a collector. Two details are randomly taken. Find the probability that at least one of them has been made by the factory № 1.
- Ao 17/38
- Bo 5/19
- Co 16/19
- Do 1/5
- Eo 1/16
4949. There are 5 details made by the factory № 1 and 15 details of the factory № 2 at a collector. Two details are randomly taken. Find the probability that at least one of them has been made by the factory № 2.
- Ao 18/19
- Bo 5/19
- Co 16/19
- Do 1/5
- Eo 1/16
5050. 10 of 20 savings banks are located behind a city boundary. 4 savings banks are randomly selected for an inspection. What is the probability that among the selected banks appears inside the city 2 savings banks?
- Ao 0.418
- Bo 0.07
- Co 0.5
- Do 0.6
- Eo 0.23
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