Homework Help is Here – Start Your Trial Now!
Math
Probability
Exercise 2.1 (Sample Space and Events) The rise times (unit: min.) of a reactor for two batches are measured in an experiment. 1. Define the sample space of the experiment. 2. Define Ei where the reactor rise time of the first batch is less than 55 min. and E2 where the reactor rise time of the second batch is greater than 70 min. 3. Find E¡ U E2, E¡ N E2, and Ei'. 4. Are Ei and E2 mutually exclusive? 5. Are Ei and E2 exhaustive? Exercise 2.2 (Probability of Joint Event) Test results of scratch resistance and shock resistance for 100 disks of polycarbonate plastic are as follows: Shock Resistance High (B) 80 Low (B') Scratch Resistance High (A) Low (A') Let A and A' denote the event that a disk has high scratch resistance and the event that a disk has low scratch resistance, respectively. Let B and B' denote the event that a disk has high shock resistance and the event that a disk has low shock resistance, respectively. 1. When a disk is selected at random, find the probability that both the scratch and shock resistances of the disk are high. 2. When a disk is selected at random, find the probability that the scratch or

Exercise 2.1 (Sample Space and Events) The rise times (unit: min.) of a reactor for two batches are measured in an experiment. 1. Define the sample space of the experiment. 2. Define Ei where the reactor rise time of the first batch is less than 55 min. and E2 where the reactor rise time of the second batch is greater than 70 min. 3. Find E¡ U E2, E¡ N E2, and Ei'. 4. Are Ei and E2 mutually exclusive? 5. Are Ei and E2 exhaustive? Exercise 2.2 (Probability of Joint Event) Test results of scratch resistance and shock resistance for 100 disks of polycarbonate plastic are as follows: Shock Resistance High (B) 80 Low (B') Scratch Resistance High (A) Low (A') Let A and A' denote the event that a disk has high scratch resistance and the event that a disk has low scratch resistance, respectively. Let B and B' denote the event that a disk has high shock resistance and the event that a disk has low shock resistance, respectively. 1. When a disk is selected at random, find the probability that both the scratch and shock resistances of the disk are high. 2. When a disk is selected at random, find the probability that the scratch or

A First Course in Probability (10th Edition)
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...
See similar textbooks
icon
Related questions
Question
Exercise 2.3 (Conditional Probability) In Exercise 2.2, find the probability that a disk has high scratch resistance (A) when it has high shock resistance (B). Exercise 2.4 (Multiplication and Total Probability Rule) Customers are used to evaluate preliminary product designs. In the past, 95% of highly successful products, 60% of moderately successful products, and 10% of poor products received good reviews. In addition, 40% of product designs have been highly successful, 35% have been moderately successful, and 25% have been poor products. Find the probability that a product receives a good review. Exercise 2.5 (Independence) For the resistance test results in Exercise 2.2, the following probabilities have been calculated: 89 40 P(A) = and P(A | B) = 100 43 Assess if events A and B are independent. Exercise 2.6 (Bayes’ Theorem) In Exercise 2.4, what is the probability that a new design will be highly successful if it receives a good review?
Transcribed Image Text:Exercise 2.3 (Conditional Probability) In Exercise 2.2, find the probability that a disk has high scratch resistance (A) when it has high shock resistance (B). Exercise 2.4 (Multiplication and Total Probability Rule) Customers are used to evaluate preliminary product designs. In the past, 95% of highly successful products, 60% of moderately successful products, and 10% of poor products received good reviews. In addition, 40% of product designs have been highly successful, 35% have been moderately successful, and 25% have been poor products. Find the probability that a product receives a good review. Exercise 2.5 (Independence) For the resistance test results in Exercise 2.2, the following probabilities have been calculated: 89 40 P(A) = and P(A | B) = 100 43 Assess if events A and B are independent. Exercise 2.6 (Bayes’ Theorem) In Exercise 2.4, what is the probability that a new design will be highly successful if it receives a good review?
Exercise 2.1 (Sample Space and Events) The rise times (unit: min.) of a reactor for two batches are measured in an experiment. 1. Define the sample space of the experiment. 2. Define Ei where the reactor rise time of the first batch is less than 55 min. and E2 where the reactor rise time of the second batch is greater than 70 min. 3. Find Ej U E2, E1 n Ez, and E1'. 4. Are Ei and E2 mutually exclusive? 5. Are Ei and E2 exhaustive? Exercise 2.2 (Probability of Joint Event) Test results of scratch resistance and shock resistance for 100 disks of polycarbonate plastic are as follows: Shock Resistance High (B) 80 Low (B') Scratch Resistance High (A) Low (A’) Let A and A' denote the event that a disk has high scratch resistance and the event that a disk has low scratch resistance, respectively. Let B and B' denote the event that a disk has high shock resistance and the event that a disk has low shock resistance, respectively. 1. When a disk is selected at random, find the probability that both the scratch and shock resistances of the disk are high. 2. When a disk is selected at random, find the probability that the scratch or shock resistance of the disk is high. 3. Consider the event that a disk has high scratch resistance and the event that a disk has high shock resistance. Are these two events mutually exclusive?
Transcribed Image Text:Exercise 2.1 (Sample Space and Events) The rise times (unit: min.) of a reactor for two batches are measured in an experiment. 1. Define the sample space of the experiment. 2. Define Ei where the reactor rise time of the first batch is less than 55 min. and E2 where the reactor rise time of the second batch is greater than 70 min. 3. Find Ej U E2, E1 n Ez, and E1'. 4. Are Ei and E2 mutually exclusive? 5. Are Ei and E2 exhaustive? Exercise 2.2 (Probability of Joint Event) Test results of scratch resistance and shock resistance for 100 disks of polycarbonate plastic are as follows: Shock Resistance High (B) 80 Low (B') Scratch Resistance High (A) Low (A’) Let A and A' denote the event that a disk has high scratch resistance and the event that a disk has low scratch resistance, respectively. Let B and B' denote the event that a disk has high shock resistance and the event that a disk has low shock resistance, respectively. 1. When a disk is selected at random, find the probability that both the scratch and shock resistances of the disk are high. 2. When a disk is selected at random, find the probability that the scratch or shock resistance of the disk is high. 3. Consider the event that a disk has high scratch resistance and the event that a disk has high shock resistance. Are these two events mutually exclusive?
Expert Solution
steps

Step by step

Solved in 2 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON
SEE MORE TEXTBOOKS