1) A box containing 3 defective resistors and three non-defective resistors are picked at random and R represents the number of defective resistors in the sample. Describe - a) the sample space S, b) the value that R assumes at each of the sample points, and c) the corresponding probabilities

Q: 18. A group of 5 boys and 10 girls is lined up in random order — that is, each of the 15!…

A: Given: A group of 5 boys and 10 girls is lined up in random order — that is, each of the 15!…

Q: In the transmission of digital information, the probabilities that a bit has high, moderate and low…

A: Given that, the probability that a bit has high distortion is 0.01. Therefore, P(A)=0.01 The…

Q: Three cards are drawn from a deck of thirty playing cards separated into threeequally portioned…

A: Concept of probability:Probability deals with the likelihood of occurrence of a given event. The…

Q: A group of 300 people are being split into teams of 3 (where order of teams and order within a team…

A: Given that: Number of people in a group, n = 300 Here, each team containing 3 people, x = 3

Q: 2. What is the minimum number of points a sample space must contain in order that there exist n…

A: Ans : Step 1.

Q: Consider three boxes containing a brand of light bulbs. Box I contains 6 bulbs of which 2 are…

A:

Q: A drum contains 4 black balls, 5 red balls and 6 green balls. If 5 balls are selected at random,…

A:

Q: Can you help me understand and solve #4?

A: Define the random variable X as the number of individuals that changes residence during the year.…

Q: 2.6 Two jurors are selected from 4 alternates to serve at a murder trial. Using the notation A1 A3,…

A: We have to select two jurors 4 alternatives Let ,  A1A2 denotes th event Alternative 1 and 2 are…

Q: In a factory that manufactures automobile tires, tires are produced in two workshops. 60% of the…

A: According to the given information, P(first workshop) = 0.60 P(second workshop) = 0.40 P(defective /…

Q: 17.-Personnel selection. Suppose that 6 female and 5 male applicants have been successfully screened…

A: Note : As per authoring guidelines, when multiple subparts are posted, then only first three…

Q: (b) The number of red balls in a sample of 8 balls chosen at random from a box contains 30 balls of…

A: We have to find the mean and variance of Hypergeometric distribution.

Q: We shall let the sample space consist of all subsets (unordered) of 10 out of the 24 light bulbs in…

A:

Q: A laboratory technician is to be tested on identifying blood types from 13 standard classifications.…

A:

Q: Consider three boxes containing a brand of light bulbs. Box I contains 6 bulbs of which 2 are…

A:

Q: ) Assume a randomly chosen battery has a probability of 0.8 of working. A remote control requires…

A: Given: Probability (working)=0.8

Q: suppose that when a new machine is functioning well, 92% of the items produced are non-defective.…

A: Probability of selecting non defective = 92% = 0.92 q= 0.92 We know that, p= 1-q= 0.08  If we select…

Q: An urn holds 10 identical balls except that 2 are white, 2 are black, and 6 are red. An experiment…

A: It is given that there are 10 balls. But only 3 types of them are there.

Q: 16. Suppose that when a machine is adjusted properly, 50 percent of the items produced by it are of…

A: Event: In probability theory, an event is an outcome or a set of outcomes of a random experiment to…

Q: On a random cross medical checkup in Muscat airport, the statisic shows 45% of the travelers are…

A: Based on the provided information, the known values are; PRegion A=0.45;PRegion B=0.35;PRegion…

Q: A woman has 10 pairs of shoes out of order and on an inopportune trip she chooses 12 shoes at…

A: Probability value of an event is between the range of values 0 to 1. The probability of an event is…

Q: Suppose 20% of all copies of a particular textbook fail a certain binding strength test. Let X…

A:

Q: According to the most recent Labor Department data, 10% of engineers (electrical, mechanical, civil,…

A: Given that,  Sample size (n) = 14 P = 10% P(x

Q: A: A box contains (3) red balls, (6) White balls ,and (9) blue balls, we draw two balls with return,…

A: Given a box contains 3 red balls, 6 white balls and 9 blue balls, draw two balls with return from…

Q: Consider a tournament between N teams, each team playing each of the other teams. Let’s call team i…

A: There are N teams Each team playing with each of the other N - 1 teams. Team i a k-winner if there…

Q: 1. a) Consider a bit string from the set of all bit strings of length ten. i. What is the…

A:

Q: 29. The registration record of a private college indicates that 40 % of its new intakes are…

A: Let X denote the number of local students are noted. Then X follows a Binomial distribution with n=…

Q: ______ denotes the observed number of persons in each cell, whereas _____ denotes the expected…

A: We have to find correct notations used to represent given sentences.

Q: 4. Consider a collection of 18 color wheels, where each color wheel has 6 colors: red, orange,…

A: Given Data: n=18 p=1/6   X~ Binomial (18, 1/6)

Q: A study is conducted at a retirement home to determine the attitudes of nurses towards various…

A: Probability is the likelihood of all the observation. That is probability is the chance of…

Q: A highway camera films cars daily as they pass by. Over a two-month period, the camera shows that…

A:

Q: Consider three boxes containing a brand of light bulbs. Box I contains 6 bulbs of which 2 are…

A:

Q: (a) A host on a cruise ship warits systematic sample of passengers? O The host forms 4 groups of…

A: Q1) Option c) is correct. The host takes a list of the passengers and selects every 4th passenger…

Q: 5. A batch of electronic parts contains 16, which are within a power tolerance and 4, which are not.…

A:

Q: Let S be a sample space with 16 possible events. If A is an event consisting of 3 outcomes of S, how…

A:

Q: Suppose a math class contains 25 students, 11 females (two of whom speak French) and 14 males (five…

A: GivenTotal no. of students = 25No. of females = 11No.of females whom speak french = 2No.of males =…

Q: Suppose a box of 40 donut holes, out of which 16 are glazed and 24 are not glazed. If the…

A:

Q: A study is conducted at a retirement home to determine the attitudes of nurses towards various…

A: We know, if there are n objects and we have to select m objects out of them then the number of ways…

Q: An urn contains seven red balls, seven white balls, and seven blue balls and a sample of five balls…

A: Given total red balls = 7Total white balls = 7Total blue balls = 7A sample of five balls is drawn at…

Q: Suppose that 20% of fruit flies possess a certain gene.  If we randomly select 20 fruit flies find…

A: Let X be the number of flies in the sample possess the gene which follows binomial distribution with…

Q: According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s are brown, 15%…

A: Hi, we are supposed to answer three subparts at a time. Since you have not mentioned which subpart…

Q: Show that in a sample space with n points, there are exactly 2^n - 1 events containing at least one…

A: Formula:Make a note of the formula: nC0 + nC1 + … + nCn = 2n.

Q: 18 Records of a credit card company show that 30% of its cardholders over age 50 dispute one or more…

A: Given,n=10p=0.30Let X=no.of cardholders dispute a charge X~Binomial(n=10 , p=0.30)P(X=x)=10x 0.30x…

Q: If two of the individuals are randomly selected without replacement, what is the probability of both…

A: HERE AS PER GUIDELINES I HAVE CALCULATED 3 SUBPARTS  here use given data table  here Rewrite table…

Q: * The result of an examination given to a class on three papers A, B and C are : 40% failed in paper…

A: Given,P(A)=0.4P(B)=0.3P(C)=0.25P(A∩B)=0.15P(B∩C)=0.12P(A∩C)=0.10P(A∩B∩C)=0.30

Q: The quality control manager at a battery factory picks three batteries at random each day from the…

A:

Q: An academic department with five faculty members narrowed its choice for department head to either…

A: Number of ways to select the votes for B:There are 2 votes for B out of 5 votes. Thus, there are 5C2…

Q: Consider three boxes containing a brand of light bulbs. Box I contains 6 bulbs of which 2 are…

A:

Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent. 

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described. 

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.