Question

Problem 1.4 You are lost in the basement of the Photonics center where the population is entirely composed of students and professors. You are looking for the exit, which youve decided is equally likely to be to the East or to the West. The students comprise two-thirds of the population, and any one student gives a correct answer to a request for directions with probability 3/4. (Assume answers to repeated questions are independent, even if the question and the person asked are the same.) If you ask a professor for directions, the answer is always wrong. (a) You ask a random person (without knowing whether they are a student or a professor) whether the exit is to the East or West. The answer returned is East. What is the proba bility that the answer would be East, given that the true direction was East? What is the probability that the answer is East, given that the true direction was West? To get started denote by E the event that the true direction is East, W that it is West, S the event that the person is a student, F for faculty, and E the event that the first answer is E. Compute P[E1 E] and PE W]. (Hint: Use the Total Probability Theorem.) (b) What is the probability the first answer East is correct? That is, compute P[E E1]. (Hint (c) You ask the same person again, and receive the same reply East. Let E2 denote the event (d) You ask the same person again, and receive now the reply West. Denote this event as Ws Use Bayes Theorem.) that this answer was East. Compute the probability that this is correct P㈣En&J Compute the probability that E is correct given these answers PEEn E2 n Ws
0 0
Add a comment Improve this question Transcribed image text
Know the answer?
Add Answer to:
Problem 1.4 You are lost in the basement of the Photonics center where the population is...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions
  • Of the students living in the dormitories at a university, 65% live in the west hall,...

    Of the students living in the dormitories at a university, 65% live in the west hall, and the rest at the south tower. A sandwich shop randomly mails a coupon for a free sandwich to 27 % of those at the west hall, and to 16% of those living at the south tower. Let D be the event that the person receives a coupon, E1 be the event that the person is living in the west hall, and E2 be...

  • Pls answer both parts. Thanks! Problem 1A (expectation and p.d.f. of a function of a random...

    Pls answer both parts. Thanks! Problem 1A (expectation and p.d.f. of a function of a random variable, Y-g(X)). Consider a random variable X~Uniformle, e2] and define the new random variable Y - In X (a) Compute E(Y), using the theorem that states that E(g(()x() dz. (b) Now we will calculate E(Y) by computing the probability density function of Y first. To do so the initial step is to figure out what the c.d.f. of Y is, by noticing that: Note...

  • Have to show work for every problem 4. A company uses three plants to produce a...

    Have to show work for every problem 4. A company uses three plants to produce a new computer chip. Plant A produces 30% of the chips. Plant B produces 45% of the chips. The rest of the chips are produced by plant C. Each plant has its own defectiv rate. These are: plant A produces 3% defective chips, plant B produces 1% defective chips, plant C produces 5% defective chips. Hint: draw a tree diagram. (a) Construct a tree diagram...

  • python 11.8 Multiple committees The eventual goal of this assignment is to compute the total number...

    python 11.8 Multiple committees The eventual goal of this assignment is to compute the total number of ways of forming a collection of committees from an academic department of n professors. The first task is to write a function called committee to compute the number of ways of forming a single committee with members from a collection of n people. This is the same as compușing the number of ways of choosing r people out of n to sit at...

  • Please try to answer all questions and show work. Thank you. 1. A baseball player is...

    Please try to answer all questions and show work. Thank you. 1. A baseball player is warming up and tosses a ball straight up into the air. The ball travels up until it reaches some maximum height, and then falls back down to the player's hand. If we neglect air resistance, then the magnitude of the acceleration of the ball is? A. largest the moment after it leaves the players hand. B. smallgst the moment after it leaves the player's...

  • 1-Suppose you write an application in which one class contains code that keeps track of the...

    1-Suppose you write an application in which one class contains code that keeps track of the state of a board game, a separate class sets up a GUI to display the board, and a CSS is used to control the stylistic details of the GUI (for example, the color of the board.) This is an example of a.Duck Typing b.Separation of Concerns c.Functional Programming d.Polymorphism e.Enumerated Values 2-JUnit assertions should be designed so that they a.Fail (ie, are false) if...

  • Nombre . Responde las siguientes preguntas A) SI P(A 6 B)-1/3 P(B)- 1/4 y P(Ay B)-1/5, halle P(A) B ) Cual es la probabilidad de lanzar un par de dados y que la suma de los result...

    Nombre . Responde las siguientes preguntas A) SI P(A 6 B)-1/3 P(B)- 1/4 y P(Ay B)-1/5, halle P(A) B ) Cual es la probabilidad de lanzar un par de dados y que la suma de los resultados de los dos dados sea 7 C ) Una prueba de selección múltiple tiene cinco posibles respuestas de las cuales una es correcta, si 13 estudiantes eligen las respuestas al azar. Cuaál es la probabilidad de que los 13 escojan la respuesta correcta?...

  • Super stuck on a couple of questions on this scenario. Advanced Scenario 7: Mark and Barbara...

    Super stuck on a couple of questions on this scenario. Advanced Scenario 7: Mark and Barbara Matthews Directions Using the tax software, complete the tax retum, including Form 1040 and all appropri- ate forms, schedules, or worksheets. Answer the questions following the scenario. Note: When entering Social Security numbers (SSNS) or Employer identification Numbers (EINS), replace the Xs as directed, or with any four digits of your choice. Interview Notes • Mark and Barbara are married and want to file...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT