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Probability

Probability : Random Selection and Conditional Probability

12. Urn I contains 2 white and 4 red balls, whereas urn II contains 1 white and 1 red ball. A ball is randomly chosen form urn I and put into urn II, and a ball is then randomly selected from urn II. What is (a) the probability that the ball selected from urn II is white; (b) the conditional probability that the transferred b

Probability

10. Ninety-eight percent of all babies survive delivery. However, 15 percent of all births involve Cesarean (C) sections, and when a C section is performed the baby survives 96 percent of the time. If a randomly chosen pregnant woman does not have a C section, what is the probability that her baby survives?

Probability

6. If there are 12 strangers in a room, what is the probability that no two of them celebrate their birthday in the same month?

Probability : Permutation and Position

4. A group of individuals containing b boys and g girls is lined up in random order?that is, each of the (b + g)! permutations is assumed to be equally likely. What is the probability that the person in the ith position, 1 ≤ i ≤ b+g, is a girl?

Probability: jailer's reasoning

40. Three prisoners are informed by their jailer that one of them has been chosen at random to be executed and the other two are to be freed. Prisoner A asks the jailer to tell him privately which of his fellow prisoners will be set free, claiming that there would be no harm in divulging this information because he already know

Proof : Probability - Independent Events

Prove or give a counterexample. If E1 and E2 are independent, then they are conditionally independent given F. Please see the attached file for the fully formatted problem.

Posterior Probability

An absent-minded nurse is to give Mr. Brown a pill each day. The probability that the nurse forgets to administer the pill is 2/3. If he receives the pill, the probability that Mr. Brown will die is 1/3. If he does not get his pill, the probability that he will die is 3/4. Mr. Brown dies. What is the probability that the nurse f

Finding Probability with Given Restrictions

12. Let E, F, and G be three events. Find expressions for the events so that of E, F, and G: (a) only E occurs; (b) both E and G but not F occur; (c) at least one of the events occurs; (d) at least two of the events occur; (e) all three occur; (f) none of the events occurs.

Find the probability of the following events.

This problems is from 400 level probability class but introductory course. Please specify the terms you use (if necessary) and explain each step of your solutions. Thank you very much. 18. 45% of the students at U of M do neither have a tattoo nor a body piercing (other than an ear piercing). 40% of the students at U of M ha

The problems are from probability class.

The problems are from 400 level probability class but introductory course. Please specify the terms you use (if necessary) and explain each step of your solutions. Thank you very much.

The problems are from probability class.

The problems are from 400 level probability class but introductory course. Please specify the terms you use (if necessary) and explain each step of your solutions. Thank you very much.

Define Independent Events

Suppose E,F are subsets of the sample space of an experiment with random outcomes of an experiment. We often call E,F events. Define what it means for E,F to be independent. (Question also included in attachment)

Find the Winning Strategy for a Coin Flip Game

Your opponent specifies 3 successives results of tosses of a coin, e.g. HHT. You then specify another such result, e.g. THT. The winner is the person whose sequence appears first when a fair coin is tossed successively and independently. Find the strategy which will allow you, the second player, to win at least 2/3 of the time.

Child Gender Probability

Assuming boy and girl children are equally likely and births are independent, if parents have two children, what is the probability that at least one is a boy? On the condition that at least one is a boy, what is the probability that one of the children is a girl?

Probability : Finitely Additive / Countably Additive

Please use words to describe the solution process. (I've attached a possibly useful review of probability). Suppose that P is finitely additive on an alegbra {field} A. Show that P is countably additive on A <---> whenever {An} is a sequence in ... *see attachment*

Probability : Proportion and Groups

Problem 8. Suppose that an insurance company classifies people into low, average and high risk persons. Their records indicate that the probabilities of being involved in an accident over a 1-year period are 0.05, 0.15 and 0.30 for low, average and high risk persons, respectively. Assume that 30% of the population is low-risk, 5

Dice probability

A random number of dice is rolled. Find the probability that... (SEE ATTACHED)

Probability

34. Jones figures that the total number of thousands of miles that an auto can be driven before it would need to be junked as an exponential random variable with parameter 1/20. Smith has a used car that he claims has been driven only 10,000 miles. If Jones purchases the car, what is the probability that she would get at least 2

Probability Density Function

Suppose X had probability density function cx^2 for 0 < x < 1, 0 otherwise. Find (a) the constant c, and the (b) mean, and (c) variance fo X.

Probability- lifetime of light bulbs

A certain factory has three machines A,B and C that produces one type of light bulbs.Past experience has shown that the lifetime of a light bulb by machine A can be modeled as an exponential random variable with an average of 20 days, whereas the lifetime of a bulb produced by a machine B can modeled as a normal random variable

Geometry : Probability that Three Points on a Circle will form a Right-Triangle

If n points are equally spaced on the circumference of a circle, what is the probability that three points chosen at random will form a right triangle? I know that for us to have a right triangle, the two points should form the diameter of the circle. What I have done is that I divided the problem into two sections. Section

Find an approximate 95% confidence interval for the mean of this distribution

It was suggested that the number of particles in a randomly selected interval might follow a Poisson distribution. Assuming a Poisson distribution to be an appropriate model for the data, use two methods to find an approximate 95% confidence interval for the mean of this distribution. See attachment for full question includin

A sample of n independent observations...

Please see the attached file for full problem description. --- ? A sample of n independent observations are obtained of a random variable having a Poisson distribution with mean . Show that the maximum likelihood estimate of is he sample mean show that the corresponding estimator is an unbiased estimator of , and h

Dice problem involving probability

Constuct an unique pair of dice (6 sides) so that each of the sums 2 through 12 has an equal (nonzero i.e. cannot have two dice with all zero's) probability of occurring. The dice do not have to be identical.