We have a bag that contains 2 red balls, 3 blue balls and 4 green balls. For our first experiment, we take a random ball from the bag, observing its colour, return the ball to the bag, and then take a second ball at random, observing its colour. i) Describe the sample space and event space for this experiment. You do not need to explicitly list every element of the event space. ii) Let BG denote the event in which the first ball drawn is blue, and the second is green. Calculate P(BG). iii) Let R denote the event in which either the first or second ball drawn is red, including the case where both are red. Calculate P(R).
We have a bag that contains 2 red balls, 3 blue balls and 4 green balls. For our first experiment, we take a random ball from the bag, observing its colour, return the ball to the bag, and then take a second ball at random, observing its colour. i) Describe the sample space and event space for this experiment. You do not need to explicitly list every element of the event space. ii) Let BG denote the event in which the first ball drawn is blue, and the second is green. Calculate P(BG). iii) Let R denote the event in which either the first or second ball drawn is red, including the case where both are red. Calculate P(R).
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 4ECP: Show that the probability of drawing a club at random from a standard deck of 52 playing cards is...
Related questions
Question
![We have a bag that contains 2 red balls, 3 blue balls and 4 green balls. For our first
experiment, we take a random ball from the bag, observing its colour, return the ball to
the bag, and then take a second ball at random, observing its colour.
i) Describe the sample space and event space for this experiment. You do not need
to explicitly list every element of the event space.
ii) Let BG denote the event in which the first ball drawn is blue, and the second is
green. Calculate P(BG).
iii) Let R denote the event in which either the first or second ball drawn is red,
including the case where both are red. Calculate P(R).
In a second experiment, we keep the same bag, but instead of returning the first ball to
the bag, we do not replace it before drawing the second.
iv) Explain how the probability space for this new experiment differs to that for the
first experiment.
v) Let R1,B1,G be the events in which, respectively, a red, blue or green ball is
drawn first, and G, the event in which a green ball is drawn second. Calculate
P(G2|R1), P(G2|B1) and P(G2|G).
vi) Using your answer from the previous question, calculate P(G2).
vii) Using Bayes' Theorem, calculate P(B||G2).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6ab89ad2-328d-4004-b31e-cca641a10119%2F49e07c74-e85d-43c4-9e8d-ffdb5f6e66ab%2Fqrc7eo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:We have a bag that contains 2 red balls, 3 blue balls and 4 green balls. For our first
experiment, we take a random ball from the bag, observing its colour, return the ball to
the bag, and then take a second ball at random, observing its colour.
i) Describe the sample space and event space for this experiment. You do not need
to explicitly list every element of the event space.
ii) Let BG denote the event in which the first ball drawn is blue, and the second is
green. Calculate P(BG).
iii) Let R denote the event in which either the first or second ball drawn is red,
including the case where both are red. Calculate P(R).
In a second experiment, we keep the same bag, but instead of returning the first ball to
the bag, we do not replace it before drawing the second.
iv) Explain how the probability space for this new experiment differs to that for the
first experiment.
v) Let R1,B1,G be the events in which, respectively, a red, blue or green ball is
drawn first, and G, the event in which a green ball is drawn second. Calculate
P(G2|R1), P(G2|B1) and P(G2|G).
vi) Using your answer from the previous question, calculate P(G2).
vii) Using Bayes' Theorem, calculate P(B||G2).
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Recommended textbooks for you
![College Algebra](https://www.bartleby.com/isbn_cover_images/9781337282291/9781337282291_smallCoverImage.gif)
![Holt Mcdougal Larson Pre-algebra: Student Edition…](https://www.bartleby.com/isbn_cover_images/9780547587776/9780547587776_smallCoverImage.jpg)
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
![College Algebra (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305652231/9781305652231_smallCoverImage.gif)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
![College Algebra](https://www.bartleby.com/isbn_cover_images/9781337282291/9781337282291_smallCoverImage.gif)
![Holt Mcdougal Larson Pre-algebra: Student Edition…](https://www.bartleby.com/isbn_cover_images/9780547587776/9780547587776_smallCoverImage.jpg)
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
![College Algebra (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305652231/9781305652231_smallCoverImage.gif)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![College Algebra](https://www.bartleby.com/isbn_cover_images/9781305115545/9781305115545_smallCoverImage.gif)
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning