Suppose that there are 3 possible states of the weather in the fall: "sunny", "cloudy" and "rainy". Suppose that if the weather is sunny on one day, then on the following day it will be sunny with probability 0.4, cloudy with probability 0.3 and rainy with probability 0.3. Moreover, if the weather is cloudy on a given day, then it will never be sunny on the following day, but it might be cloudy again with a probability of 0.8 or rainy with a probability of 0.2. Finally, if the weather is rainy on any given day, it will be sunny on the following day with a probability of 0.2, cloudy with a probability of 0.3 and rainy with a probability of 0.5. a) Write the transition matrix A corresponding to the Markov chain described above. b) On any given day, what is the transition matrix B describing the probabilities of being in the states "sunny", "cloudy" and "rainy" two days from now?

Q: Suppose at a local dentist office is open 7 days a week and an average of 84 patients are seen in a…

A: The random variable X is patients seen in a week. The average number of patients seen in a week is…

Q: A customer visiting the suit department of a certain store will purchase a suit with probability…

A: a)It is given that, a certain store will purchase a suit with probability 0.22, a shirt with…

Q: Consider a shopper will choose either brand A or brand B. On each purchase, the probability that he…

A:

Q: Suppose that it is equally likely for a couple to have a boy or a girl.   (a) Suppose a couple has…

A: Consider that, equally likely for a couple to have a boy or a girl. (a) Consider that  couple has…

Q: Suppose there are 500 people coming to an event that will be giving away 5 door prizes. The 145th…

A: Given Total no of people in event= 500 The 145th person to walk through the doors will get $100, the…

Q: Two events, A and B, are mutually exclusive and each has a nonzero probability. If event A is known…

A: Mutually Exclusive events: Events which cannot occurs together are called mutually exclusive events.…

Q: Suppose that in a year of 365 days, it rains on 34 days. There is lightning on 19 days. There is…

A: Given that ; N = 365 days Rains = 34 days  Lighting = 19 days  Both = 12 days By using the basic…

Q: Suppose that 70% of students in Prof. Leen’s statistics class do their homework regularly and 65%…

A:

Q: Suppose that it is equally likely for a child to be a boy or a girl. Suppose a parent tells you that…

A: Given information- We have given that it is equally likely for a child to be a boy or a girl.…

Q: ingredients. Additionally, suppose that the flavor of the pastry changes based on the order the…

A: solution:

Q: Assume that a box contains 2 defective widgets and 12 acceptable widgets. There are 4 inspectors,…

A: Given that there are 2 defective widgets and 12 acceptable widgets in the box. So total (2+12)=14…

Q: Suppose that it is equally likely for a child to be a boy or a girl. Suppose a parent tells you that…

A:

Q: Suppose a box contains 1 green ball and 1 red ball, and a second box contains2 green and 3 red…

A: NowA1 : First box chosenA2 : second box chosenP(A1)=P(A2)=1/2=0.5NowFirst box has 1 green ball and 1…

Q: If A, B are mutually exclusive events, then the probability that A does NOT occur given that B…

A: if A and B are mutually exclusive events then A∩B=∅ i.e. P( A∩B)=0 let A¯ is complement of A. now,…

Q: XYZ auto insurer company offers an auto insurance plan to the employees of a company. The employees…

A: The company offers an auto insurance plan of a company. The employees cannot choose exactly two of…

Q: Suppose a family consisting of a father and a son plays a "Gambler's ruin" game for the Chinese New…

A: Let:q be the probability of the father winning a token.p be the probability of the son winning a…

Q: When a certain basketball player takes his first shot in a game he succeeds with probability 1/2. If…

A: ANSWER: From the given data,

Q: When two events cannot occur at the same time, they are said to be ?

A: Disjoint events:   Let A and B be any two events, if the events A and B are mutually exclusive or…

Q: Suppose that it is equally likely for a child to be a boy or a girl. Suppose a parent tells you that…

A: Let us denote B=boy and G=girl Given that at least 4 of the children are girls. So the possible…

Q: Suppose that there is a white urn containing two white balls and three red balls and there is a red…

A: Given that white urn contains  white balls and  red balls and red urn contains 2 white ball and 4…

Q: uppose that there is a white urn containing three white balls and one red ball and there is a red…

A:

Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent. 

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described. 

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.