#### Question Details

(solution) Hello! I have a few quick questions on probability, please,

Hello! I have a few quick questions on probability, please, numbers 1, 3, 6, 7, 8. I figured out the ones in the book. Thank you!

Math 180A - Homework 2

( Due Friday, OCT 7, 2:00 PM)

Reading: Sections 1.1 - 1.5 and 2.5 of the textbook and lecture notes 4-6.

Show FULL JUSTIFICATION for all your answers. 1. In how many ways can 8 people be seated in a row if

a. there are no restrictions on the seating arrangement;

b. persons A and B do NOT want to sit next to each other;

c. there are 4 married couples and each couple must sit together.

2. Problem 17. of Chapter 2. of the textbook.

3. An urn contains 12 red balls and 6 black balls. If we choose 5 balls at random from the urn,

what is the probability that at least 2 black balls will be among the 5 balls chosen?

4. Problem 31. of Chapter 2. of the textbook.

5. Problem 29. of Chapter 2. of the textbook.

6. Provide a purely combinatorial argument (requiring little or no computations) to establish

the following identity for an integers n ? 1:

X

n

i?1

n

=

k?1

k

i=k (Hint: consider the event Ai that when you choose k numbers from the set {1, ..., n}, the

largest number chosen is i)

7. Provide a purely combinatorial explanation of why

n

n

=

r

r, n ? r

8. a. Suppose 8 cards are chosen at random from one deck of playing cards. What is the

probability that exactly 2 cards are chosen from each suit.

b. Now suppose we have 8 sets of playing cards, and we choose one card at random from

each set. What is the probability that, among 8 cards chosen, there are exactly 2 cards

from each suit.

c. Compare the results of parts a and b: which of the two cases has a bigger probability?

Provide a heuristic argument for why such is the case. 9. Problem 54. of Chapter 2. of the textbook.

10. Fill out the Survey No. 2 in TritonEd. 1

**Solution details:**

Answered

QUALITY

Approved

ANSWER RATING

This question was answered on: * Sep 13, 2020 *

* * Solution~00021147652353.docx (25.37 KB)

##### Pay using PayPal (No PayPal account Required) or your credit card . All your purchases are securely protected by .

#### About this Question

STATUSAnswered

QUALITYApproved

DATE ANSWEREDSep 13, 2020

EXPERTTutor

ANSWER RATING

#### GET INSTANT HELP/h4>

We have top-notch tutors who can do your essay/homework for you at a reasonable cost and then you can simply use that essay as a template to build your own arguments.

You can also use these solutions:

- As a reference for in-depth understanding of the subject.
- As a source of ideas / reasoning for your own research (if properly referenced)
- For editing and paraphrasing (check your institution's definition of plagiarism and recommended paraphrase).

#### NEW ASSIGNMENT HELP?

### Order New Solution. Quick Turnaround

Click on the button below in order to Order for a New, Original and High-Quality Essay Solutions.
New orders are original solutions *and precise to your writing instruction requirements. Place a New Order using the button below.*

WE GUARANTEE, THAT YOUR PAPER WILL BE WRITTEN FROM SCRATCH AND WITHIN A DEADLINE.