by restrictingexperiment, without changing 2.available to the observer of theExercisesWe start with some warm-up exercises arranged by section.Section 1.1Exercise 1.1. We roll a fair die twice. Describe a sample space and a proba-bility measure P to model this experiment. Let A be the event that the secondroll is larger than the first. Find the probability P(A) that the event A occurs.Exercise 1.2. For breakfast Bob has three options: cereal, eggs or fruit. He hasto choose exactly two items out of the three available.(a) Describe the sample space of this experiment.Hint. What are the different possible outcomes for Bob's breakfast?(b) Let A be the event that Bob's breakfast includes cereal. Express A as asubset of the sample space.Exercise 1.3.(a) You flip a coin and roll a die. Describe the sample space of this experiment.(b) Now each of 10 people flips a coin and rolls a die. Describe the samplespace of this experiment. How many elements are in the sample space?(c) In the experiment of part (b), how many outcomes are in the event wherenobody rolled a five? How many outcomes are in the event where at leastone person rolled a five?Section 1.2Exercise 1.4. Every day a kindergarten class chooses randomly one of the 50state flags to hang on the wall, without regard to previous choices. We areinterested in the flags that are chosen on Monday, Tuesday and Wednesday ofnext week.

Exercise 1.1. We roll a fair die twice. Describe a sample space 2 and a proba- bility measure P to model this experiment. Let A be the event that the second roll is larger than the first. Find the probability P(A) that the event A occurs.

Exercise 1.1. We roll a fair die twice. Describe a sample space 2 and a proba- bility measure P to model this experiment. Let A be the event that the second roll is larger than the first. Find the probability P(A) that the event A occurs.

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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Question

by restricting
experiment, without changing 2.
available to the observer of the
Exercises
We start with some warm-up exercises arranged by section.
Section 1.1
Exercise 1.1. We roll a fair die twice. Describe a sample space and a proba-
bility measure P to model this experiment. Let A be the event that the second
roll is larger than the first. Find the probability P(A) that the event A occurs.
Exercise 1.2. For breakfast Bob has three options: cereal, eggs or fruit. He has
to choose exactly two items out of the three available.
(a) Describe the sample space of this experiment.
Hint. What are the different possible outcomes for Bob's breakfast?
(b) Let A be the event that Bob's breakfast includes cereal. Express A as a
subset of the sample space.
Exercise 1.3.
(a) You flip a coin and roll a die. Describe the sample space of this experiment.
(b) Now each of 10 people flips a coin and rolls a die. Describe the sample
space of this experiment. How many elements are in the sample space?
(c) In the experiment of part (b), how many outcomes are in the event where
nobody rolled a five? How many outcomes are in the event where at least
one person rolled a five?
Section 1.2
Exercise 1.4. Every day a kindergarten class chooses randomly one of the 50
state flags to hang on the wall, without regard to previous choices. We are
interested in the flags that are chosen on Monday, Tuesday and Wednesday of
next week.

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Note: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a time so we are answering the first one as you have not mentioned which one you are looking for. Please re-submit the question separately for the remaining question.

Given that,

The experiment is to roll a fair die twice.

The event $A$ is the second roll is larger than the first.

The sample space is the set of all possible outcomes of the event.

The probability is the ratio of the number of favorable outcomes of the event to the total number of outcomes.

The sample space of roll a fair die

$Ω = {1, 2, 3, 4, 5, 6}$

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