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Help pls with probability tasks.

1.In the class, there are 14 girls and 9 boys. Let's consider event A - there are at least two girls in the class who were born in the same month. Event A is...
A. an impossible event
C. an elementary event
B. a certain event
D. impossible to determine

2.There are 75 parts in the box, each labeled with a number from 1 to 75. Among these parts, 10 are defective. Let's consider event B - taking out a part with the number 10 from the box. Event B is...
A. an impossible event
B. a certain event
C. an elementary event
D. impossible to determine

3.Out of 25 shots, 20 hit the target. The relative frequency of hits is...
A. 5/25
B. 5/20
C. 25/20
D. 20/25

4.In a certain month, 43 boys and 57 girls were born. The relative frequency of boys born in that month is...
A. 43/57
B. 57/43
C. 43/100
D. 57/100

5.There are twelve balls in a jar, labeled with numbers from 1 to 12. The probability that drawing a ball will result in a number divisible by 3 is...
A. 1/12
B. 1/4
C. 1/3
D. 1/2

6.The probability that a part is of good quality is 0.75. Calculate the probability that it is not of good quality.
A. 0.25
B. 1
C. 0.75
D. 0.25/0.75

7.Two coins are flipped. The probability that at least one coin lands heads up is...
A. 0.25
B. 0.5
C. 0.75
D. 1

8.A fair die is rolled. The probability of rolling a 2 is...
A. 1/6
B. 5/6
C. 1/3
D. 2/3

9.From a deck of cards containing 36 cards, one card is drawn. Calculate the probability that the drawn card is a spade.
A. 1/4
B. 1/6
C. 1/9
D. 1/36

10.There are 2 white and 8 black marbles in a bag. Calculate the probability of randomly selecting a white marble.
A. 1/5
B. 1/4
C. 3/4
D. 1/36

11.Two dice are rolled. Calculate the probability that the sum of the numbers rolled is 5.
A. 1/36
B. 1/9
C. 5/36
D. 1/6

12.Jānis usually throws a ball into the basket with a probability of 0.68. Calculate how many times he will throw the ball into the basket if he makes 50 throws.
A. 8
B. 16
C. 34
D. 0.44

13.Two dice are rolled. The probability that at least one of them shows 4 points is...
A. 1/6
B. 1/9
C. 11/36
D. 1/3
14.A worker regulates two independent machines. The probability of needing to regulate the first machine within an hour is 0.8, and for the second machine it is 0.7. Calculate the probability that both machines need to be regulated within an hour.
A. 0.44
B. 0.56
C. 0.2
D. 0.3

15.Targets are arranged in two concentric rings with radii R and 4R. It is known that a shot hit the target. Calculate the probability that the shot hit the smaller ring.
A. 1/4
B. 1/3
C. 1/16
D. 1/9

16.In a lottery with 20 tickets, 4 tickets are winning tickets. Ilze buys one ticket. Calculate the probability that her ticket is a winning ticket.
A. 1/4
B. 1/5
C. 1/20
D. 4/5

17.Two friends meet. Calculate the probability that both of them were born on a Saturday.
A. 1/7
B. 2/7
C. 2/49
D. 1/49

18.A student has learned 7 out of 8 questions. In a test, two of these questions will be included. Calculate the probability that the student knows both of these questions.
A. 7/8
B. 49/56
C. 42/64
D. 3/4

19.There are 4 cards in an envelope labeled with the letters A, P, S, E. Successively, three cards are drawn from the envelope without replacement. Calculate the probability that the cards are drawn in the order A, P, E.
A. 1/6
B. 1/12
C. 1/24
D. 3!/4!

20.Two dice are rolled simultaneously. Calculate the probability that the sum of the numbers rolled is 14.
A. 1
B. 14/36
C. 1/36
D. 0

User ARKBAN
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1 Answer

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Explanation:

Event A is a certain event because with 14 girls and only 12 months in a year, by the pigeonhole principle, there must be at least two girls who were born in the same month.

Event B is an elementary event because there is only one part labeled with the number 10 out of 75 parts in the box, so the probability of drawing that part is 1/75.

The relative frequency of hits is calculated by dividing the number of hits by the total number of shots. In this case, it is 20/25.

The relative frequency of boys born in that month is calculated by dividing the number of boys born by the total number of births. In this case, it is 43/100.

There are four balls labeled with numbers divisible by 3 (3, 6, 9, and 12) out of twelve balls in total. So the probability of drawing a ball with a number divisible by 3 is 4/12 = 1/3.

The probability that a part is not of good quality is equal to 1 minus the probability that it is of good quality. In this case, it is 1 - 0.75 = 0.25.

The probability that at least one coin lands heads up is equal to 1 minus the probability that both coins land tails up. The probability that both coins land tails up is (1/2) * (1/2) = 1/4. So the probability that at least one coin lands heads up is 1 - 1/4 = 3/4.

A fair die has six equally likely outcomes when rolled. So the probability of rolling a 2 is 1/6.

A deck of cards containing 36 cards has four suits: clubs, diamonds, hearts, and spades. Each suit has nine cards, so there are nine spades in the deck. So the probability of drawing a spade is 9/36 = 1/4.

There are two white marbles and ten marbles in total in the bag. So the probability of randomly selecting a white marble is 2/10 = 1/5.

There are four ways to roll two dice and get a sum of five: (1,4), (2,3), (3,2), or (4,1). Each outcome has a probability of (1/6) * (1/6) = 1/36. So the probability that the sum of the numbers rolled is five is 4 * (1/36) = 1/9.

If Jānis throws a ball into the basket with a probability of 0.68 and he makes 50 throws, we can expect him to throw the ball into the basket about 0.68 * 50 = 34 times.

The probability that at least one die shows four points when two dice are rolled can be calculated as one minus the probability that neither die shows four points: P(at least one die shows four points) = = 1 - P(neither die shows four points) = 1 - P(first die does not show four points) * P(second die does not show four points) = 1 - (5/6) * (5/6) =11/36

If two events are independent, then the probability that both events occur simultaneously can be calculated as the product of their probabilities: P(both machines need to be regulated within an hour) = = P(first machine needs to be regulated within an hour) * P(second machine needs to be regulated within an hour) =0.8 *0.7 =0.56

15.The area of a circle is proportional to the square of its radius so if we consider each ring as a target then their areas will be proportional to R^2 and (4R)^2 respectively. The ratio between these areas will be R^2 : (4R)^2 = R^2 :16R^2 =1:16 So if we consider each unit area as having an equal chance to be hit then we have: P(the shot hit the smaller ring)= Area(smaller ring)/(Area(smaller ring)+Area(larger ring))=1/(16+1)=1/17

16.There are four winning tickets out of twenty tickets in total in a lottery so if Ilze buys one ticket then her chance to get a winning ticket will be: P(Ilze’s ticket is a winning ticket)= Number of winning tickets / Total number of tickets=4/20=1/5

17.The day on which someone was born can be any day from Monday to Sunday with equal chances so if we consider two friends then: P(both friends were born on Saturday)=P(first friend was born on Saturday)P(second friend was born on Saturday)=(1/7)(1/7)=1/49

18.The student knows seven out of eight questions so if two questions are included in a test then his chance to know both questions will be: P(the student knows both questions)= Number of ways to choose two known questions / Number of ways to choose any two questions=(7 choose 2)/(8 choose 2)=21/28=3/4

19.There are four cards labeled with letters A,P,S,E so if three cards are drawn successively without replacement then there will be: Number of ways to draw three cards=Number of ways to draw first cardNumber of ways to draw second cardNumber of ways to draw third card=432=24 The only way for these cards to be drawn in order A,P,E will be if they are drawn successively as A,P,E so: P(the cards are drawn in order A,P,E)=Number of ways for cards to be drawn in order A,P,E / Number of ways for any three cards to be drawn=1/24

20.Two dice have six faces each so when they are rolled simultaneously there will be: Number of possible outcomes=Number of faces on first dieNumber of faces on second die=66=36 None of these outcomes will result in a sum equal to fourteen so: P(the sum of numbers rolled equals fourteen)=0

User Cppanda
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