CSIT 270 Homework 6
Q1.1
Ans 1.1 If S is a finite sample space of equal likely outcomes and E is an event , that is a subset of S
Then the probability of E is :
P(E) =
The probability that a five-card poker hand does not contain the queen of hearts is determined as follows:
If 5 cards are drawn then chances of not getting the queen of hearts in the first draw is
If there is no chance getting the queen of hearts in drawn and the chance of not getting it in 2nd draw is
If there is no chance getting the queen of hearts in drawn and the chance of not getting it in 3rd draw is
If there is no chance getting the queen of hearts in drawn and the chance of not getting it in 4th draw is
If there is no chance getting the queen of hearts
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a) The probability of no failures
b) the probability of at least one failure
c) the probability of at most one failure
d) probability of at least two failures
Ans 5:
Given that n independent Bernoulli trails are carried out with probability of success being p
The probility of failure is 1 – p
( a) : The probability of no failure is the same as the probability of all sucessess
(b): The probability of atleast one failure is the sum of probability of 1,2,3,……. N failures which is the same as deductiong no failures from total probablility 1
1-
(c): the probabiltyi of atmost one failure is the sum of the probability of most one failure
+ + n(1-p)
(d):
The probability that there are atleast 2 failures is the sum of the probabilities of 2,3, ….. n failures
It is the same as subtracting the probabilities of 1 and 0 failures from the total probability 1.
1- [ +
= 1- [ + n(1-p)]
6. Suppose that E and F are events in a sample space and p(E)=1/3, p(F)=1/2 and p(E|F)=2/5. Find
1b. You get the same prize but the choice changes to $5,000 now or $5,500 in three years. What do you do?
Frank Stockton’s short story “ The Lady or the Tiger” is about how a “semi-barbaric king” punishes those who commit a crime by putting them in an arena.The accused must choose one out of two doors. He will either open one of the doors awaited by the beautiful bride who was searched all over the land to find the perfect fit for him. Or open the door that holds a vicious beast that is about to attack him and devour him in a split second. A handsome young man in this kingdom ends up on trial because he dared to love and win the king’s daughter’s heart. The princess having a “ soul as imperious and fervent as the king” ,knows which door holds the vicious beast and which holds the beautiful bride. There is supporting evidence that the
| An undergraduate business student has purchased a laptop computer for use during exams. This laptop is perfectly reliable except for two parts: its microchip, which has a failure rate of one in every twenty hours of operation; and its battery, which has a failure rate of one in every ten hours of operation. In addition, on average the battery will wear out in five hours, with a standard deviation of 30 minutes. Assuming that a new battery has just been installed, what is the probability that the battery will perform reliably during a one-hour exam?Answer
As QUEEN you have to promise to follow the QUEENs Doctrine. The QUEENs Doctrine tells you about being QUEEN.
Caroll also hints that Queen Victoria is most likely to convict an innocent man or woman to prison due her inability to judge and give the correct punishment as she is often sway by her emotions. The author further juxtaposes Queen Victorian and The Queen of Hearts by accentuating the fact that Queen Victoria is ruthless and vicious when it pertains to punishments. Not only Queen Victoria is known for her overbearing attitude, she can juxtapose due to her love for punishment and judging a crime unfairly just like the Queen of Hearts. “‘You may go, ‘said the King, to the Hatter hurriedly left the court, without even waiting to put his shoes on—and just take his head off outside,’ the Queen added to one of the officers (Through the Looking Glass 102). Caroll uses the Queen of Hearts to satirises Queen Victoria because Caroll would have find her ridiculous with her flaws that makes her incompetent as a Queen. All in all, Queen of Hearts is a character that is parallel to Queen Victoria to deride and ridicule the ruler of Britain during the Victorian
In ‘Once Upon a Time’, the Queen of Hearts is once the daughter of a miller called, Cora. She tells the king that she can make straw into gold. And the King promises if she can do it the next day, he will let the prince marry her. In order to achieve the commitment, she asks the Dark one for help. The Dark one teaches her magic, and she marries to the prince successfully. Since then, she uses magic to achieve her goals. She rips her own heart out so that nothing could stop her. (season 2, episode 9) And she controls her daughter through the magic and claim that is for her own good. One day, her daughter cannot tolerate her anymore and push her into a looking glass. Cora arrives the Wonderland, and eventually controls it. She becomes the Queen
A number of years ago in 1978 there was a movie that starred Warren Beatty. It was called Heaven Can Wait. Throughout the film, there was a common theme of probability and outcome. It kept showing how the probability of something happening seemed almost certain however; the outcome was different in many cases than one would have thought it to be.(Beatty, Beatty, & Henry, 1978)
The cards were new to raising a kid so they didn't know that they could say no. Everything she asked for she got. The cards did not want to be mean so they did whatever she asked. The queen of hearts did not have any friends, or even enemies there was no one. Just her and the 5 cards her whole child hood. She got bored sometimes, so she made the cards put on a show for her. She had no idea what spoiled was.
She went to the first town closest to the castle. Elissa sent a messenger the day before to the town to announce to the lady umbrella the queen was looking for the next queen and the requirements they MUST have. The following day the queen went and saw the line of girl umbrellas. She went to the front of the line and sat down and began assessing the first lady and so and so on. The queen found not one umbrella fit for the duty new and future queen on Mistmoor. The queen had gone through town 1, 2, 3, 4, and 5 she came to six town and did the same thing sent a messenger to inform the ladies to have the requirement that the queen wants. As the queen saw the line of ladies in line to stand before her she saw a very bizarre umbrella. The queen tried and hurried to get to this one particular umbrella. When the very particular umbrella came up, she the beauty, but none of the other requirement that the queen wanted but that one. The queen was so disappointed she finally gave up and didn't bother for the rest of the day to look for a future queen. Elissa had gone to 7, 8, and 9 finally she had gotten to town 10. Once again and for the last and final time the queen sent a messenger to the ladies of the town what the queen wanted. When the queen was walking in one of the guards who wasn’t one of hers attacked her. The assassin was apprehended and taken to the town dungeon. The guard that was on duty was telling the
The Queen had left very detailed instructions as to how she wanted her funeral. The instructions included very specific things she wanted inside her coffin. Many of the items she wanted were from her beloved husband,
Abstract--A number of software fault tolerance methods have been proposed to achieve high reliability. However, these methods suffer from the lack of considering the possibility of correlated failures, where the failure of multiple components leads to system failure. Furthermore, previous methods to assess the impact of correlated failure on software fault tolerance require extensive testing of data and are therefore less suitable to conduct reliability analysis in the early design stages. Hence, these types of failures must be explicitly incorporated into reliability analysis. The influence of correlated failures on application reliability must be analyzed within the context of the application architecture. This paper provides a survey of some of the studies conducted so far in the field of software reliability and gives a summary of the models proposed to study the impact of correlated failures on the software reliability. The paper concludes by highlighting the major contributions of some studies and provides a direction for the future study in the field.
2.4.1 Conditional Probability 2.4.2 Independent Events and MultiplicationRule 2.4.3 Theorem of Total Probability and Bayes Theorem
Competition exists in every field, to keep ahead a major challenge is availability improvement of a system, as less availability has negative impact. People often use “availability” and “reliability” interchangeably. In fact, however, the two terms are related but have