4. Six balls are thrown in four distinct squares. Represent the fundamental set in the followingtwo cases.(a) The ballsare numbered from 1 to 6.(b) The balls are identical.

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Answered: 4. Six balls are thrown in four…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The integers from 1 to 7 are written in order clockwise around a circle. I start with a counter on number 1 and repeatedly roll a standard six-sided fair die. If the die shows 1 then I move the counter to the next number clockwise around the circle; if the die shows 2 or 3 then I move the counter to the next number anticlockwise around the circle; if the die shows 4, 5 or 6 then I do not move the counter. (i) Describe how to model this process as a discrete-time Markov chain. Write the transition matrix (ii) Explain why the Markov property is satisfied and give an example of how you could make a small modification after which the process would be a discrete-time Markov chain which is not homogeneous.
Permutations Use the permutations to solve the given problem. Explain your answer. Show your solution. 1) There are 6 plates numbered 4, 5, 6, 7, 8, and 9. a) If you choose 3 plates out of 6 and arrange them in a row, how many three-digit numbers can be formed? b) If you choose 3 plates out of 6 and arrange them in a row, how many different three-digit odd numbers can be formed? c) you choose 3 plates out of 6 and arrange them in a row, how many different three-digit numbers larger than 700 can be formed? Show your solution.
52. Shaking Hands in a Group A group of six strangers sat in a circle, and each one got acquainted only with the person to the left and the person to the right. Then all six people stood up and each one shook hands (once) with each of the others who was still a stranger. How many handshakes occurred?
An electronic company manufactures electrical resistors with Rave = 40 Q and SD= 2, same unit. What is the probability that the manufactured products will exceed 43 Q? Assume normal distribution. O 17.24% O 82.76% O 93.32% O 6.68%
Consider these sets: A={2,7,3,1, 4} and B={8,5,7,2}. What is n(A)+n(AnB) equal to? 8 7. acer
3. How many different arrangements are there using all the letters in the word COMBINATORICS. A. 6.23×10⁹ B. 7.78×108 C. 1.56x10⁹ D. 1.25×10¹0
2. (a) A sack contains 50 marbles of 4 different colors. Explain why there are at least 13 marbles of the same color. (b) If exactly 8 of the marbles are red, explain why there are at least 14 of the same color.
How many ways are there to arrange the 26 letters of the alphabet so that no pair of vowels appear consecutively (Y is considered a consonant)?
2. I found some bingo cards in our classroom. A bingo card seems to have 5 rows and 5 columns. The center cell is blank, but the remaining cells each contain a number. No two cells contain the same number. In the first column, integers from 1 to 15 are used. In the 2nd column, integers from 16 to 30 are used, and so on. Thus, in the 5th column, integers from 61 to 75 are used. How many different bingo cards are there? Explain.

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4. Six balls are thrown in four distinct squares. Represent the fundamental set N in the following two cases. (a) The balls are numbered from 1 to 6. (b) The balls are identical.