Prove that k() = n(1) (n = 1) for integers n and k with 1 ≤ k ≤ n, using a: a) combinatorial proof;

Q: Af the probability of an event is 0.5, then the probability of the complement event will be 0.5.…

A: Answer :- If the probability of an event is 0.5, then the probability of the complement event will…

Q: or equal to 5 is 1 3 How many cards are in the bag?

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Q: A random sample of size 25 is taken from a normal population having a mean of 85 and a standard…

A: Solution-: Given: n1=25,μ1=85,σ1=2,n2=81,μ2=75,σ2=6 We want to find the sample mean computed from…

Q: What is the range of all integers greater than 40 and less than 99 that are multiples of 3

A: To find : The range of all integers greater than 40 and less than 99 that are multiples of 3

Q: You are given 5 to 1 odds against tossing three tails with three coins, meaning you win $5 if you…

A: Given data you are given 5 to 1 odds against tossing three tails with three coins you win $5 if you…

Q: A binomial experiment consists of 700trials. The probability of success for each trial is 0.6. What…

A:

Q: The population of Boomtown is currently 2000 and expected to grow by 2.7% over the next year. What…

A: Given that ; For Boomtown   Current population (P) = 2000 Growth rate = 2.7% For Dullsville…

Q: h. Find the conditional distribution of f (x[y), P(X = 2 | Y = 1). i. Find the conditional…

A: here given joint distribution of x and y  Using bayes rule Calculate the conditional Distribution

Q: B: Which of the following values cannot be probabilities of events and why? 4 4 0.87,-0.95,…

A: To find:  Which of the following values cannot be probabilities of events and why?

Q: What is the minimal number of people needed in a class to ensure that there are two students with…

A: Given information: To ensure that there are two students with the same birthday (the same month and…

Q: Suppose a drawer contains five brown socks, seven blue socks, and four red socks. We draw one sock…

A: The answer is attached below,

Q: Jean puts 12 books on a shelf in random order. Three are by the same author. What is the probability…

A: Given:12 books on a shelf in random order.3 are by the same auther.Find:P( books will be next to…

Q: If Andrei checks his pulse for 4 minutes, what is his rate if he counts 284 beats?

A: We have given that Total minutes = 4 Total beats count = 284 Rate is given by Rate = Total number of…

Q: The number of combinations of 3 items selected from 8 is 122. Select one: O True O False Give your…

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Q: The sample space of a random experiment is the set of positive real numbers, S={x|x>0}. Define…

A:

Q: chloe's bookshelf has 6 books by Smith and 8 books by jones. if she removes 4 books at random, what…

A: Given data: Total books = 6 +8  = 14 She removes 4 books randomly To find: The probability of…

Q: What is 113 % of 105? Identify the percent, the base, and the amount. Write the percent as a…

A: Given that,What is 113% of 105 ?

Q: In a certain city, the daily consumption of electric power, in millions of kilowatt-hours, is a…

A: Given:Define,X:Daily consumption of electric power in millions of kilowatt-hours.X follows gamma…

Q: Assume that a procedure yields a binomial distribution with n=3 trials and a probability of success…

A: The answer is attached below,

Q: At a certain gas station, 65% of the customers use regular gas, and all the other customers use…

A: Given Information: 65% of the customers use regular gas. Of those only 30% fill their tank.…

Q: Determine if the proportion is true 16 20 41 50 O Proportion is true O Proportion is not true Submit…

A: It is given that the proportion. Here, need to check the given proportion is true or not.

Q: B: A card is drawn from a well shuffled pack of 52 cards. Find the probability of: (i) '2' of…

A: GivenTotal no.of cards = 52

Q: Actual and Relative Change The value of a car dropped from $37,800 to $35,200 over the last year.…

A: Given that  The value of a car dropped from $37,800 to $35,200 over the last year. Previous year…

Q: nas, III past, its goblets. Such goblets are designated as "seconds". Assume defective goblets are…

A: It is given that p = 0.10.

Q: The sample space of a random experiment is the set of positive real numbers, $={xx >0}, Define…

A: The similarity and dissimilarity between the finite sets are understand using set theory. Set denote…

Q: A box contains a total of 100 CDs that were manufactured on two machines. Of them, 60 were…

A:

Q: ose the heights of 18-year-old men are approximately normally distributed, with mean 69 inches and…

A: Here, μ=69 and σ=5. (a) The probability that an 18-year-old man selected at random is between 68 and…

Q: Using empirical probability, suppose you tossed a fair coin 450 times and noted that it landed on…

A: From the provided information, Total number of times a fair coin is tossed = 450 It is noted that it…

Q: Compute the following probabilities: (a) Pr(X= $3 Y = t₁) (b) Pr(X= $2) (c) Pr(Y= t1)

A: HERE AS PER GUIDELINES I HAVE CALCULATED  3 SUBPARTS  here given  join distribution of variable t…

Q: Enter the ratio as a fraction in lowest terms 90 minutes to 80 minutes

A:

Q: When playing basketball, Dwight makes 80% of his free throws. In a recent game Dwight attempted 30…

A: Given data when playing basket ball Dwight makes 80% of his free throws in a recent game Dwight…

Q: Problem 2. To fulfill the requirements for a certain degree, a student can choose to take any 7 out…

A: There are 20 courses in total. One has to choose 7 out of 20 courses such that at least one of them…

Q: If a multiple-choice test consists of 5 questions each with 4 possible answers of which only one is…

A: Solution Given That, if a multiple choice test consists of 5 questions each with 4 possible answers…

Q: The average number of cars arriving at a drive-thru fast food restaurant is 3 in ten minutes, what…

A: GivenAn average no.of cars arriving at a drive-thru fast food restaurant is 3 in tenminutesλ=1.5 for…

Q: A thrifty hospital administrator purchased 2 refurbished back-up generators to power the hospital in…

A: Given,P(1st generator  reliability rate)=0.77P(2nd generator  reliability rate)=0.87and two…

Q: In a fruit juice company, machine A (crusher) produces 45%, Machine B (juice extractor) produces…

A: We have to given that,  Machine A, B, and C are did work 45% , 30% and 25% of total work…

Q: 78% of the questions on a student's test were correct. There were 50 questions. How many of the…

A: Given  Total number of questions =50 Percentage of correct questions =78%

Q: What is the probability that a set of n ≥ 2 has two permutations that are the reverse of one…

A:

Q: Ona multiple choice test with 5 questions, each question has three possible answers, one of which is…

A: Answer : -  Given,  n = 5  questions, each question has three possible answers,…

Q: Kilie is an avid collector of action figures based on superhero movies. She has been tracking the…

A: Given datakilie is an avid collector of action figures based on superhero movies

Q: 3. Let us consider Y = X₁(X₁+X₂), where X₁ and X₂ are two independent Bernoulli random variables…

A: Given that X1 and X2 are independent Bernoulli random variables with parameter p=1/4. That is,…

Q: region representing planes x = a1, Find the probability that a point (X, Y, Z) lands in a a hollow…

A:

Q: The failure of a car's engine follows a Weibull distribution. Such failure rate is described by a…

A: Solution  Given That, The failure of a car's engine follows a Weibull distribution. Such failure…

Q: Let f(x) = 0, C:C x² +1¹ 0, if x ≤ 0 if 0<x<√e-1. if x ≥ √e-1 For what value of c is f(x) a…

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Q: U=1, find the conditional expecta n U = 1, find the conditional expecta = 1, find the conditional…

A: Given: U and V be independent random variable.

Q: 2 You need to borrow money for gas, so you ask your mother. Before giving you money, she makes You…

A: Given that the spinner has evenly divided wedges with three red, two green and one blue.

Q: On a hiking trip, the ratio of the number of children to the number of adults is 3 to 5. Which of…

A:

Q: Find the value of E, the margin of error, for c= 0.95, n = 10 and s= 3.9. ents A. 2.261 0 OB. 2.79…

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Q: A particle starts from the origin and moves in a certain direction for a distance 1₁. Then it…

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Q: Use the given statement to represent a claim. Write its complement and state which is Ho and which…

A: From the provided information, The statement of the hypothesis is as follow: µ ≥ 203