Prove that, for any probability space (2, B, P) and events A, B E B, if Р () P(B) 1 P(AN B) " P(An B) P(A) ' P(B)

Q: suppose that for a particular flight, an airline believes that 2%2% of ticket holders do not make…

A: Given information- Number of passengers a jet hold = 189 Number of tickets sold = 192 Percentage of…

Q: let E be an event for which P(E)>0. Show that the conditional  probability in P(*/E) satisfies the…

A: The axioms are related to the probability theory.

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 machines turn on all the products in a factory with the first machine producing 30% of the…

A: Given, Three machines turn on all the products in a factory with the first machine producing 30% of…

Q: A box contains 12 transistors of type A and 18 of type B, all identical in appearance. If one…

A:

Q: in a plant, 30% of the employees work in the assembly hall, 20% work in the offices, and 40% are…

A: The question is about probability for given events Given : Prob. of the employees work in assembly…

Q: 10 involving a student's attendance at math and accounting classes on Mondays. Assume that the…

A: Let us assume that: A= attending math class B= attending accounting class   Given that P(A)=0.55,…

Q: Theorem 3-13. Necessary and sufficient condition for independence of n events A1, A2, ..., An is…

A:

Q: 26% of all college students major in STEM (Science, Technology, Engineering, and Math). If 49…

A: From the provided information, 26% of all college students major in STEM. That is p = 0.26 Sample…

Q: Suppose that n enemy aircraft are shot at simultaneously by m gunners, that each gunner selects an…

A: From given information : Let x denote the number of aircraft hit by gunners. Let us define x: to be…

Q: A player of a video game is confronted with a series of four opponents and an 80% probability of…

A: A players of a video game is confronted with with series of four opponents.  There is 80%…

Q: 6. Let A1 denote the event that no red balls are selected, let A2 denote the event that no white…

A:

Q: The Wayne Manufacturing Company purchases a certain part from suppliers A, B, and C. Supplier A…

A: The conditional probability of happening of event A when event B already happened, can be expressed…

Q: Most restaurants offer lower-priced meals that are available on weekdays. However, only 65% of all…

A: Given info: Most restaurants offer lower-priced meals that are available on weekdays. However, only…

Q: If 20% of the bolts produced on a machine are defective, determine the probability that 4 randomly…

A: Let X be the number of defective  Let p be the probability of defective  p= 20%, n=sample size  n=4…

Q: If X is a random variable having a geometric distribu-tion, show that P(X = x + n|X > n) = P(X =…

A:

Q: A company knows that 25% of it customers are retirees. Find the probability that if 7 of this…

A:

Q: Let Aj denote the event that no red balls are selected, let A2 denote the event that no white balls…

A:

Q: Suppose that 4% of the patients tested in a clinic are infected with avian influenza. Furthermore,…

A:

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

A: Given that  Box contains  Red balls = 2 Green balls = 3 Blue balls = 2 Total balls in box = 7 We…

Q: Calculate the probability that exactly eight of the customers have purchased any one of the two…

A: The probability that a customer will purchase any of the two products    p=P(A)(1-P(B) +P(B) (1-P(A)…

Q: Let N = {1,2,3, 4, 5, 6}, A = {1,2,3}.Define P(A) = .How far can it extend this probabilistic…

A:

Q: At a certain gas station, 40% of the customers use regular gas (A,), 35% use plus gas (A,), and 25%…

A: As per our guidelines, we are allowed to answer first three sub-parts only. Thanks Given : P(A1) =…

Q: There are 3 targets and 2 shooters. Shooter 1 will fire at either targets 1 or 2, each with…

A: Let the 3 targets be T1, T2 and T3. And the 2 shooters be S1 and S2. P[S1 hits T1]=0.5=P[S1 hits T2]…

Q: The resumes of two male applicants for a college teaching position in Engineering Data Analysis are…

A: Given Information: The resumes of two male applicants are placed in the same file as the resumes of…

Q: It is known that 40% of a certain company's washing machines require service while under warranty,…

A:

Q: The third postulate of probability is sometimes referred to as the special addi- tion rule; it is…

A:

Q: 22% of all tires manufactured by a company are defective. If 20 different tires are randomly…

A: INTRODUCTION :   BINOMIAL DISTRIBUTION: let X be a discrete random variable  let x be the number of…

Q: Each of three persons fires one shot at a target. The outcomes of the shots made by them are…

A: The event is each three persons fires one shot at a target. Consider Ai denote the event that person…

Q: Let us assume that 30% of the population of people own Suzuki-made Cars, and 20% own cars from other…

A: 30% of the population has Suzuki car so P(Suz)=0.30 and 20% has car of other company so POther=0.20.…

Q: Each of N boxes contains w white balls and b black balls. A ball is chosen at random from Box 1 and…

A: Given Information: Total number of boxes =N. Number of white balls in each box =w. Number of black…

Q: A particular slot machine in a casino has payouts set so that the probability of winning money in…

A:

Q: 34% of all college students major in STEM (Science, Technology, Engineering, and Math). If 45…

A: Note:Please repost part d as i can answer only 3 subparts as per my policy.   Given data,…

Q: An urn contains 8 blue balls, 1 green and 1 white ball. Suppose you independently draw 11 balls,…

A: Given data: The numbers of blue balls are B=8. The number of the green ball is G=1. The number of…

Q: It is known that 40% of a certain company's washing machines require service while under warranty,…

A: Formula : P(A n B) = P(A).P(B)

Q: At a company a central computer is used in half of the working time in accountancy related to…

A:

Q: 27% of all college students major in STEM (Science, Technology, Engineering, and Math). If 39…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…

Q: In a certain factory, machines I, II, and III are all producing springs of the same length. Machines…

A: Obtain the probability that it is defective if one spring is selected at random from the total…

Q: A certain delivery requires 2 trucks. Suppose that a randomly selected truck will be mechanically…

A: From the given information, the required trucks for delivery is 2. P(older truck)=p=0.5 P(newer…

Q: Let H be the event that a job candidate is hired, and let Q be the event that a job candidate is…

A: Given that H = the event that a job candidate is hired Q = the event that a job candidate is well…

Q: P(A1) = 0.22, P(A2) = 0.25, P(A3) = 0.28, P(A1 ∩ A2) = 0.14, P(A1 ∩ A3) = 0.04, P(A2 ∩ A3) = 0.07,…

A: (a). Express the given event in words and compute the probability: The given event is A1c ∩ A2c ∩…

Q: A major video distributor purchases blank DVDs from two​ sources: Retailer​ A, which provides 72% of…

A: Given information, P(Retailer A)=0.72 P(Retailer B)=0.38 P(defective| Retailer A)=0.04 P(defective|…

Q: A local drugstore owner knows that, on average, 100 people enter his store each hour. (a) Find the…

A: Given that, A local drugstore owner knows that, on average, 100 people enter his store each hour.

Q: found that 20% of the total pens bought are defective. There are 5 defecti defective blue pens. 250…

A: Construct contingency table from given information.

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

A:

Q: In a certain factory, machines I, II, and III are all producing springs of the same Q.2. length.…

A:

Q: There are 12 apples in a basket. 5 of these apples are rotten. If a person randomly selects 4 apples…

A: Given Data: Let X represent the number of rotten apples p=5/12   n=4 X~ Binomial (4, 5/12)   Let Y…

Q: 2. Suppose that a box initially contains b black balls and w white balls. In each step, we select a…

A: Box -  (  b black balls and w white balls) One ball drawn, put it back with one new of same colour.…

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.