A rat is placed in the maze shown below, and it moves from room to room randomly. From any room, the rat will choose a door to the next room with equal probabilities. Once it reaches room 1, it finds food and never leaves that room. And when it reaches room 5, it is trapped and cannot leave that room. What is the probability the rat will end up in room 5 if it was initially placed in room 3?
A survey of computer buyers indicates that if a person buys an Apple computer, there is an 80% chance that their next purchase will be an Apple, while owners of an IBM will buy an IBM again with a probability of .70. The buying habits of these consumers are represented in the transition matrix below.
Find the following probabilities:
The probability that a present owner of an Apple will buy an IBM as his next computer.
The probability that a present owner of an Apple will buy an IBM as his third computer.
The probability that a present owner of an IBM will buy an IBM as his fourth computer.
Professor Trayer either teaches Finite Math or Statistics each quarter. She never teaches Finite Math two consecutive quarters, but if she teaches Statistics one quarter, then the next quarter she will teach Statistics with a
$1/3$ probability.
Write a transition matrix for this problem.
If Professor Trayer teaches Finite Math in the Fall quarter, what is the probability that she will teach Statistics in the Winter quarter.
If Professor Trayer teaches Finite Math in the Fall quarter, what is the probability that she will teach Statistics in the Spring quarter.
The transition matrix for switching academic majors each quarter by students at a university is given below, where Science, Business, and Liberal Arts majors are denoted by the letters
$S$ ,
$B$ , and
$A$ , respectively.
Find the probability of a science major switching to a business major during their first quarter.
Find the probability of a business major switching to a Liberal Arts major during their second quarter.
Find the probability of a science major switching to a Liberal Arts major during their third quarter.
John Elway, the football quarterback for the Denver Broncos, calls his own plays. At every play he has to decide to either pass the ball or hand it off. The transition matrix for his plays is given in the following table, where
$P$ represents a pass and
$H$ a handoff.
Find the following.
If John Elway threw a pass on the first play, what is the probability that he will handoff on the third play?
Company I, Company II, and Company III compete against each other, and the transition matrix for people switching from company to company each year is given below.
Find the following.
If the initial market share is 20% for Company I, 30% for Company II and 50% for Company III, what will the market share be after the next year?
If this trend continues, what is the long range expectation for the market?
A rat is placed in the maze shown below, and it moves from room to room randomly. From any room, the rat will choose a door to the next room with equal probabilities. Once it reaches room 1, it finds food and never leaves that room. And when it reaches room 6, it is trapped and cannot leave that room. What is the probability that the rat will end up in room 1 if it was initially placed in room 3?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
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8. It is known that 80% of the people wear seat belts, and 5% of the people quit smoking last year. If 4% of the people who wear seat belts quit smoking, are the events, wearing a seat belt and quitting smoking, independent?
Mr. Shamir employs two part-time typists, Inna and Jim for his typing needs. Inna charges $10 an hour and can type 6 pages an hour, while Jim charges $12 an hour and can type 8 pages per hour. Each typist must be employed at least 8 hours per week to keep them on the payroll. If Mr. Shamir has at least 208 pages to be typed, how many hours per week should he employ each student to minimize his typing costs, and what will be the total cost?
At De Anza College, 20% of the students take Finite Mathematics, 30% take Statistics and 10% take both. What percentage of the students take Finite Mathematics or Statistics?