Q8) Suppose that the probability of rain today depends on weather conditions from theprevious three days. If it has rained for the past'three days, then it will rain today withprobability 0.7; if it did not rain for any of the past three days, then it will rain today withprobability 0.1; if it rained each of the past two days but not three days ago, it will rain withprobability 0.8; and, in any other case, the weather today will match yesterday's weatherwith probability 0.6.

Answered: Image /qna-images/answer/8c80b2a0-0ef9-4db9-a8b3-74ae839c4186.jpg

Answered: 88) Suppose that the probability of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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7. Suppose that there is 50% chance that it will rain today and 60% chance that it will rain tomorrow. Suppose also that there is 30% chance that it will rain both days. The probability that it either will rain today or tomorrow, but not both, is A. 0.5 B. 0.6 C. 0.3 D. 0.1
Suppose that there is a white urn containing two white balls and three red balls and there is a red urn containing two white balls and four red balls. An experiment consists of selecting at random a ball from the white urn and then (without replacing the first ball) selecting at random a ball from the urn having the color of the first ball. Find the probability that the second ball is red.
3) In a recent semester at a local university, 530 students enrolled in both General Chemistry and Calculus I. Of these students, 53 received an A in general chemistry, 83 received an A in calculus, and 25 received an A in both general chemistry and calculus. Find the probability that a randomly chosen student received an A in general chemistry or calculus.
Suppose that an employee at a local company checks his watch and realizes that he has 10 minutes to get to work on time. If he leaves now and does not get stopped by any traffic lights, he will arrive at work in exactly 8 minutes. In between his house and his work there are three traffic lights, A, B, and C. Each light that stops him will cause him to arrive an additional 2 minutes later. The following table displays the probability that he is stopped by each of the three traffic lights. Assume that the probability that he is stopped by any given light is independent of the probability that he is stopped by any other light. Traffic light A Traffic light B Traffic light C ?(?)P⁡(A) ?(?)P⁡(B) ?(?)P⁡(C) 0.6 0.4 0.9 What is the probability that the employee is not late for work? (Round to 3 decimal places)
3. A retailer sells two brands of batteries that experience indicates are equal in demand. If he stocks two of each brand (which means he has 4 batteries in his store), what is the probability that a customer seeking to purchase two batteries, purchases the same brand? 1/3 2/3 01/2 1/4
Suppose that each time Bar-bie throws a dart, she has a 3/4 probability of getting a bullseye. If Barbie shoots three darts, what is the probability that she gets a bullseye on at least two of them?
1) A particular gadget contains 50 integrated circuits (ICs). The probability that any one of these ICs is defective is 0.02. The gadget will function only if there is no defective IC. What is the probability that the gadget will function?
9. A law firm employs three types of lawyers: junior lawyers, senior lawyers, and partners. During a given year, there is a 0.1 probability that a junior lawyer will be promoted to senior lawyer and a 0.05 probability that he or she will leave the firm. Also, there is a 0.2 probability that a senior lawyer will be promoted to partner and a 0.15 probability that he or she will leave the firm. There is a 0.03 probability that a partner will leave the firm. The firm never demotes a lawyer. th Let Xn be the status of an employee at the n' year after he or she has been hired, it could be one of the three types of lawyers (junior, senior, or partner) or two types of leaving (either leaving as a partner or leaving as a non-partner). Let state 0-junior, state 1-senior, state 2=partner, state 3= leave as non-partner, state 4= leave as partner The (one-step) transition matrix is P = 0.85 0 0 0 0 0.1 0 0.05 0.65 0.2 0.15 0 0.97 0 0 1 0 0 0 0 0 0 0.03 0 1 (a) Use the fundamental matrix method,…
3. You get a haircut from Barber Shop 1 30% of the time and Barber Shop 2 70% of the time. Barber Shop 1 gives a good haircut 80% of the time and a bad haircut 20% of the time while Barber Shop 2 gives a good haircut 90% of the time and a bad haircut 10% of the time. For any given haircut, the probability that it is a bad haircut from Barber Shop 1 is Barber Shop 2 is and the probability that it is a good haircut from O.06; .63 .2; .73 O.06; .73 .2; .63
5. Suppose you live in an extremely unfortunate climate where it always rains on weekends (Saturday and Sunday). For that matter, there is always a chance of rain on a weekday (Monday-Friday) as well. If you have completely forgotten which day of week it is (so that it is equally likely to be any of the seven days), but you go outside and see that it's raining, what is the probability that it's the weekend?
Suppose there are exactly three states of weather: sunny, cloudy, or rainy. If it is sunny today, then the probability is 3/4 that it will be sunny tomorrow, 1/8 that it will be cloudy tomorrow, and 1/8 that it will be rainy. If it is cloudy today, then the probability is 1/2 that it will be sunny tomorrow, 1/4 that it will be cloudy tomorrow, and 1/4 that it will be rainy. If it is rainy today, then the probability is 1/4 that it will be sunny tomorrow, 1/2 that it will be cloudy tomorrow, and 1/4 that it will be rainy. cloudy is From this Markov model, for any given day the probability that it will be sunny is rainy is Round your answers to three decimal places. and
1.Mayank plays exactly one sport everyday. It can be football or basketball or chess. Forhim, the probability of playing chess on a random day is twice as that of playing footballand one third of the probability of playing basketball. What is the probability that in thenext week, he will play basketball in 3 days, chess in 2 days and football in the remainingdays?

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