### Probability

The probability that a family with 6 children has exactly four boys is: a. 1/3 b. 1/64 c. 15/64 d. 3/8 e. none of the above

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The probability that a family with 6 children has exactly four boys is: a. 1/3 b. 1/64 c. 15/64 d. 3/8 e. none of the above

The number of events associated with a sample space having "n" outcomes is: A. n b. n to the 2nd power c. 2 to the "nth" power d. n! e. none of the above

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. If there is anything unclear in the problem, please tell me. Thank you very much.

18. A true-false question is to be posed to a husband and wife team on a quiz show. Both the husband and the wife will, independently, give the correct answer with probability p. which of the following is a better strategy for the couple? (a) Choose one of them and let that person answer the question; or (b) have them both con

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

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?

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?

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?

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

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.

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

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.

19. A retail establishment accepts either the American Express or VISA credit card. A total of 24 percent of its customers carry an American Express card, 61 percent carry a VISA card, and 11 percent carry both. What percentage of its customers carry a credit card that the establishment will accept?

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 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 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.

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)

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.

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?

Suppose a pair of dice are flipped. Find the probability for each of the following events: 1. The sum of the dots is even. 2. The sum of the dots is at least 5.

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*

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

Prove Boole's inequalities.

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

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

Your lab is working to produce a particular chemical reaction. The conventional probability for producing this reaction successfully is p = ½. You have a new technique that you believe will produce this reaction successfully at least 2/3 of the time. You plan to test your method with a sequence of 36 trials. You decide to r

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.

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

Suppose the number of electrons X counted by an optical communication system is a poisson random variable .(see the wholeproblem in the attachment)

Al, Bob and Carlos are playing a silly game. Al flips a coin. If he gets heads, the game ends and he wins. If not, Bob flips the coin. If he gets heads, the game ends and he wins. If not, Carlos flips the coin. If he gets heads, the game ends and he wins. If not, the coin is returned to Al and the entire process begins a