Q3 a) A component has an exponential time to failure with a mean of 100 hours. (i) The component has already been in operation for its mean life. What is the probability that it will fall by 150 hours? (ii) The component will operate for another 50 hours given that it is in operation 150 hours. (iii) If 20 components are tested, what is the probability that at least one fails in less than 200 hours? Assume that the components fail independently. b) Students of National University were classified according to their favorite color: Blue 12 5 Favorite color Red 13 13 Black 25 20 Male Female If one student is selected at random, then find the probability that the selected student: (i) Doesn't like black color. (ii) Is Female and likes blue color. (iii) Is Male or like black color. (iv) Likes red color given that it is female.
Q3 a) A component has an exponential time to failure with a mean of 100 hours. (i) The component has already been in operation for its mean life. What is the probability that it will fall by 150 hours? (ii) The component will operate for another 50 hours given that it is in operation 150 hours. (iii) If 20 components are tested, what is the probability that at least one fails in less than 200 hours? Assume that the components fail independently. b) Students of National University were classified according to their favorite color: Blue 12 5 Favorite color Red 13 13 Black 25 20 Male Female If one student is selected at random, then find the probability that the selected student: (i) Doesn't like black color. (ii) Is Female and likes blue color. (iii) Is Male or like black color. (iv) Likes red color given that it is female.
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...
Related questions
Question
Transcribed Image Text:Q3
a) A component has an exponential time to failure with a mean of 100
hours.
(i) The component has already been in operation for its mean
life. What is the probability that it will fall by 150 hours?
(ii) The component will operate for another 50 hours given that it
is in operation 150 hours.
(iii) If 20 components are tested, what is the probability that at
least one fails in less than 200 hours? Assume that the
components fail independently.
b) Students of National University were classified according to their
favorite color:
Blue
12
5
Favorite color
Red
13
13
Black
25
20
Male
Female
If one student is selected at random, then find the probability that the
selected student:
(i) Doesn't like black color.
(ii) Is Female and likes blue color.
(iii) Is Male or like black color.
(iv) Likes red color given that it is female.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step 1: Given information
VIEWStep 2: Determine parameter of exponential distribution and distribution function
VIEWStep 3: Calculate probability that it will fall by 150 hours
VIEWStep 4: Calculate probability that another 50 hours given that it is operation 150 hours
VIEWStep 5: Calculate probability at least one component fails
VIEWStep 6: Calculate probability
VIEWStep 7: Calculate probability is female and likes blue color
VIEWStep 8: Calculate probability male or likes black color
VIEWStep 9: Calculate probability that likes red color given that it is female
VIEWSolution
VIEW
Step by step
Solved in 10 steps with 17 images
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON