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.

Consider an experiment that consists of determining the type of job—either blue-collar or white-collar—and the political affiliation—Republican, Democratic, or Independent—of the 15 members of an adul

16. Consider an experiment that consists of determining the type of job—either blue-collar or white-collar—and the political affiliation—Republican, Democratic, or Independent—of the 15 members of an adult soccer team. How many outcomes are (a) in the sample space; (b) in the event that at least one of the team members is a b ...continues

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 ...continues

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

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?

Frequency Distributions : Newspaper Readership

20. A certain town of population size 100,000 has 3 news papers: I, II, and III. The proportions of townspeople who read these papers are as follows: I: 10% I and II: 8% I and II and III: 1% II: 30% I and III: 2% III: 5% II and III: 4% (The list tells us, for instance, that 80 ...continues

21. If P(E) = 0.9 and P(F) = 0.8, show that P(EF) ≥ 0.7. In general, prove Bonferroni’s inequality, namely, P(EF) ≥ P(E) + P(F) – 1.

21. If P(E) = 0.9 and P(F) = 0.8, show that P(EF) ≥ 0.7. In general, prove Bonferroni’s inequality, namely, P(EF) ≥ P(E) + P(F) – 1.

Dividing gifts

5. In how many ways can a man divide 7 gifts among his 3 children if the eldest is to receive 3 gifts and the others 2 each?

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.

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.

Probability : Sampling with Replacement

2. An urn contains 5 red, 6 blue, and 8 green balls. If a set of 3 balls is randomly selected, what is the probability that each of the balls will be (a) of the same color; (b) of different colors? Repeat under the assumption that whenever a ball is selected, its color is noted and it is then replaced in the urn before the next ...continues

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?