A biology professor has two graduate assistants help-ing her with her research. The probability that the older of the two assistants will be absent on any given day is0.08, the probability that the younger of the two will beabsent on any given day is 0.05, and the probability thatthey will both be absent on any given day is 0.02. Find theprobabilities that(a) either or both of the graduate assistants will be absenton any given day;(b) at least one of the two graduate assistants will not beabsent on any given day;(c) only one of the two graduate assistants will be absenton any given day.

Q: Gertrude owns a movie theatre in the town of Northern Millstone. Assume the following to be true.…

A: From the given information, If a resident of Northern Millstone patronizes Gertrude’s movie theatre…

Q: Mary and Susan are each to play a tennis match. Let the probability that Mary wins her match be 0.65…

A:

Q: Jim has to take two consecutive exams to get a certificate. The probability for him to pass the…

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

Q: You have relatives coming for dinner this weekend.  The probability that your uncle Josiah will show…

A: given data  event A: uncle josiah show up B : aunt beatrice show up   P(A) = 0.48 P(B) = 0.43 P(A∩B)…

Q: Machines A and B produce 40% and 60% respectively of the production of a component intended for the…

A: Conditional Probability: Let A and B be two events with P(A) > 0. Then the conditional…

Q: The events of A and B are mutually exclusive. Suppose P(A) = 0.15 and P(B) = 0.35. What is the…

A: Given Information: The events A and B are mutually exclusive. P(A) = 0.15 and P(B) = 0.35 Two events…

Q: John finds a bill on his desk. He has three options: ignore it and leave it on his own desk, move…

A: Given that

Q: The probability of being offered the first job is 0.25, and the probability of being offered the…

A: Given data: Let X be the number of jobs offered. The probability of being offered the first job is…

Q: The probability that a contractor will get a plumbing contract, is 2/3 and the probability that he…

A: We have given that,  Let probability that a contractor will get a plumbing contract P(A) = 2/3 and…

Q: A and B are two independent events. The probability that both occur simultaneously is 1/6 and the…

A:

Q: Every day, Rick either gains two pounds (with probability 1/2 ) or loses one pound (with probability…

A: Given that Every day, Rick either gains two pounds (with probability 1/2 ) or loses one pound (with…

Q: Alicia believes that the probability for the stock market to go down is 0.7 give: that the economy…

A: We have find  gíven probability...

Q: A student is applying to Harvard and Dartmouth. He estimates that he has a probability of .5 of…

A: Solution: From the given information, P (Accepted by Dartmouth) = 0.5, P (Accepted by Harvard) = 0.3…

Q: Suppose that the probability that Bob will go downtown is  45%.  Now, also suppose that if Bob goes…

A: Given, Suppose that the probability that Bob will go downtown is  45%.  Now, also suppose that if…

Q: Suppose that an employee at a local company checks his watch and realizes that he has 10 minutes to…

A: Multiplication rule for independent events:If two events A and B are independent then the…

Q: Each time a shopper purchases a tube of toothpaste, he chooses either brand A or brand B. Suppose…

A:

Q: When a customer enters a drugstore, the probabilities that he or she will have 0, 1, 2, or 3…

A: 1. Given: The probability of persons having 0 prescription is 0.55, 1 prescription is 0.30, 2…

Q: One of the 3 shooters is randomly chosen to hit the target once. For each shooter the probabilities…

A: E1: First shooter        P(E1) = 1/3 E2: Second Shooter  P(E2) = 1/3 E3: Third Shooter     P(E3) =…

Q: An office has 2 fire detectors. Suppose that 3 out of every 100 fire detectors will fail to go off…

A: It is given that, 3 out of every 100 fire detectors will fail to go off during a fire.

Q: what is the probability that George will be elected?

A: Here given, In an upcoming congressional election, two democrats, Al and Bill, seek the nomination…

Q: On any particular Friday evening, the probability  that Jason will go to the mall and go for a…

A: event A : go to the mall event B : go for a coffee P(A∩B) = 13P(B|A) = 47P(A) = ?

Q: The probability that a shopper will buy a PS3 is 0.40. The probability that a shopper will buy an…

A: Let; PS = PS3 XB = X-Box 360 ND = Nintendo DS Given that; P(PS)=0.40P(XB)=0.54P(ND)=0.30P(PS ∩…

Q: You have relatives coming for dinner this weekend.  The probability that your uncle Josiah will show…

A: Given Data: Let A be the event that your uncle Josiah will show up Let B be the event that your aunt…

Q: Suppose that two persons are working on a project together. The probability that person A works for…

A: Given

Q: I hit two traffic lights on my way to work each morning. Both lights operate independently. The…

A: Let,  Ri : i th traffic light is red , i=1, 2Rci : i th traffic light is not red , i=1, 2   P(R1∩R2)…

Q: If the probability of being hospitalized during a year is 0.25. Find the probability that no one is…

A: X has binomial distribution. X~binomial(n,p)n=3p=0.25probability mass function of X;…

Q: Erik, Jordan, Adam, Myra, Gabriel, and Johanna have all been invited to a dinner party. They arrive…

A: Given that, 6 members are invited for a party and stated that  Adam arrives first and Erik arrives…

Q: f Mary is late for school one particular day of the week, the probability she arrives on time the…

A: Given Data: P( late the next day | on time the previous day)=0.3 P( late the next day | late the…

Q: A couple has two children, and the older child is a boy. If the probabilities of having a boy or a…

A:

Q: Alicia believes that the probability for the stock market to go down is 0.7 given that the economy…

A: Define the events, A : Economy deteriorates during Pandemic covid-19 B : Stock market go down Given…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.