There are 33 natural numbers. Prove that you can choose several numbers between them, so that their sum is divisible by three and eleven. It should be possible to solve the problem by the Dirichlet's principe.

Q: a certian states license plate has 3 letters followed by 4 numbers. repeats are not allowed for…

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Q: How many random arrangements can be obtained using come together?

A: Total letters in CONCEPT = 7 If two C's come together, consider both as a single word. Total letters…

Q: Eleven red balls and three blue balls are in a bag. If four balls from the bag are to be selected…

A: If the balls are selected without replacement, then the probability of selecting 1st red ball is,…

Q: Three balls are randomly and independently tossed into bins numbered with the positive integers so…

A: Observe that  the probability of two  or more independent events  happening together is given  by…

Q: uppose a population has N items and n items are selected with replacement. Number of all possible…

A: Given that, Population has N items and n items are selected with replacement Number of all possible…

Q: What if the researcher decided to ignore the random selection procedures as described in the example…

A: Given that the population list consisting of 50,000 women. A sample of size n = 200 is to be…

Q: Three people are chosen at random from a group of five men and ten women. What is theprobability…

A: Given, three people are chosen at random from a group of five men and ten women.

Q: A positive integer not greater than 1000 is randomly selected. What is the probability of the…

A:

Q: Compute the expected number of tests necessary for each group. Expected number for each group:

A: Answer:- Let's define a random variable X that marks the number of tests for some certain group.…

Q: Assume that 4 digits are selected at random from the set {1,2,3,5,8} and are arranged in random…

A: To compute the probability of the required event from the basic counting principles

Q: If two states are selected at random from a group of 20 states, determine the number of possible…

A:

Q: A sequence of 10 bits are randomly generated. What is the probability that there are at most two…

A:

Q: In a lottery game, a player will pick at random a number from the set {1, 2, 3, 4, 5, 6, 7, 8, 9,…

A: Set of number to pick is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.  The number picked is prime, the player…

Q: In an experiment where 2 balls are drawn successively at random without replacement from a box…

A: The total number of balls is 2+3+2 =7

Q: A particular kind of bacterium either splits into 3 bacte- ria of the same kind or dies, with…

A: Utilizing Bernoulli distribution

Q: If 4% of the bottles produced by a company are defective.determine the probabilkities of sample that…

A: Given,n=100p=0.04q=1-p=1-0.04=0.96x=no. of defectivesx~Binomial(n=100,p=0.04)P(X=x)=Cxn px qn-x   ;…

Q: Two jurors are selected from 4 alternates to serve at a murder trial. Using notations J1 and J2 to…

A: Given data: Two jurors are selected from 4 alternates to serve at a murder trial. Using notations J1…

Q: There are a total of 19,935 IRSC students, 72% of which are under the age of 25. In a random sample…

A:

Q: A six-sided die is loaded in a way that each even face is twice as likely as each odd face. All even…

A: Let, A is the event of having an even number face on the die. B is the event of having an odd number…

Q: ) To determine whether or not they have a certain disease, 130 people are to have their blood…

A: Given, Total people = 130 Each group has 10 people P(person having disease) = 0.09

Q: Assume a finite population has 2000 elements. Starting with the eleventh row (84649, 48968, 75215,…

A: As finite population has 2000 elements. There are 4 digits in 2000. So we draw a sample of digits 4.…

Q: A maths examination consists of two papers, which are marked independently. The mark given for each…

A: It is an important part of statistics. It is widely used.

Q: A lottery selects 2 digits from 0-9 without replacement. What is the probablilty that all 2 digits…

A:

Q: Two transistors are chosen at random from 12 transistors of which 4 are defective. Find the…

A: Given, Total number of transistors = 12 Defected number of transistors = 4 Crn=n!(n-r)!n!

Q: There are 12 red balls and 11 blue balls in a bowl. Without looking at the balls, a woman chooses…

A: Solution We have given that  12 red ball and 11 Blue balls  Part 1 As there are 2 colours of balls…

Q: Two balls are to be drawn in succession without replacement from an urn containing 5 red balls and 6…

A: Introduction: Total number of balls in the urn is 11 [= 5 red + 6 blue]. Since the balls are drawn…

Q: coin is flipped three times. Y is a random variable that assigns 3 times the number of heads flipped…

A: We want to find numbers is assigned to HHT

Q: Two cards are drawn at random without replacement from an ordinary deck of 52 cards. Let X be the…

A: Given: X = number of hearts Y = number of red cards n (total) = 52 n (hearts) = 13 n (red) = 26…

Q: In a lottery game, a player will pick at random a number from the set {1, 2, 3, 4, 5, 6, 7, 8, 9,…

A: It is given that the set is 1,2,3,4,5,6,7,8,9,10 Therefore the probability of picking prime is 410…

Q: only 10th , 11th and 12th grade students attend a high school the ratio of 10th graders to the…

A: Given information:The ratio of 10th graders to the school’s total population is 86:255.The ratio of…

Q: A computer system uses 4 digits numerical (from 0 to 9) passwords to provide access for resources,…

A:

Q: Suppose we have an ant travelling on edges of a cube, going from one vertex to another. The ant…

A: Look at the distance from the origin after an even number 2k of minutes. This distance can only be 0…

Q: What is the probability that the integer chosen is divisible by atleast one of the numbers 2,4,6,7?

A: Number of first 80000 positive integer divide by 2 = n(A) = 80000/2 =40000 Number of first 80000…

Q: Assume that 4 digits are selected at random from the set {1,2,5,6,7,8,9}{1,2,5,6,7,8,9} and are…

A:

Q: Suppose a COVID-19 is 85% sensitive and 82% specific. That is, the test will produce 85% true…

A: Let us define some events A : a person has the virus. B : a person does not have the virus. E : a…

Q: Three letters are to be selected at random from the English alphabet of 26 letters. Determine the…

A: Given: Three letters are to be selected at random from the alphabet of 26 letters.  Determine the…

Q: A sample of 51 planes will be taken from an infinite population. The population proportion equals…

A: Solution: From the given information, n=51 and p=0.85.

Q: Suppose that a laboratory test on a blood sample yields one of two results, positive or negative. It…

A: P(D) = probability of disease= 0.01 P(not disease) = probability of not disease= 0.99…

Q: A number from 1-50 is chosen at random. What is the probability that it is a perfect square or a…

A: We have given total number from 1- 50 i.e. Total number of outcomes = 50

Q: 9 Give exanple of a seguemce of random an Variables which converpes in distn'bution but not in…

A: In convergence in distribution, the random variables can be defined on different probability spaces,…

Q: Suppose there are a million cars made by a car company across the globe, where the probability that…

A: Given : Sample size = n = 10,00,000 probability of success = p = 0.0002 λ = np = 10,00,000 (0.0002)…

Q: If two states are selected at random from a group of 10 states, determine the number of possible…

A: With replacement, the first choice would be any of the 10 and so would the second. For this do…

Q: In a lottery game, a player will pick at random a number from the set {1, 2, 3, 4, 5, 6, 7, 8, 9,…

A: It is given that the set is 1,2,3,4,5,6,7,8,9,10 Therefore the probability of picking prime is 410…

Q: Suppose that we roll three (six-sided) dice 600 times. Find an approximation for theprobability that…

A: Introduction: Suppose an experiment consists of n independent trials, the outcome of each of which…

Q: Assume that the box contains balls numbered from 1 through 28, and that 3 are selected. A random…

A: We make a table Number of oddballs (a) Number of even balls (b) X=3a+4b 0 3 12 1 2 11 2 1…

Q: A smartphone manufacturer admits that 12% of the smartphones they make have defects that could…

A: Given that 12% of the smartphones have defects. So probability of finding a defective smartphone is…

Q: A statistician wants to obtain a systematic random sample of size 63 from a population of 6645. What…

A: K=N/n Next number=I+(n-1)K

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.