1. On this problem, give exact answers using both fractions and exact decimals. One card is chosen from a set of cards that have ranks 1 to 6. Let X be the number on the card chosen. The distribution function for picking the cards is given as follows: m(1) = 6/100, m(2) = 33/100, m(3) = 11/100, m(4) = 37/100, m(5) = 8/100, m(6) = 5/100. Let E be the event "A card with an odd numbered rank is drawn," and F be the event "A card whose rank is less than or equal to 3 is drawn." (a) Compute P(E). (b) Compute P(F). (c) Before you compute P(Eʼn F), explain (in whole sentences) whether or not it is safe to use the formula P(E^ F) = P(E) · P(F) before knowing the answer to part (g). (d) Compute P(EΜF). (e) Compute P(F|E). (f) Compute P(E|F). (g) Based on some of your answers to parts (a), (b), (e), and (f), explain (in whole sentences) whether events E and F are independent or not. In your response, please write down which probabilities you are comparing, whether they are equal or not, and how their equality or difference shows that the events E and F are independent or not.
1. On this problem, give exact answers using both fractions and exact decimals. One card is chosen from a set of cards that have ranks 1 to 6. Let X be the number on the card chosen. The distribution function for picking the cards is given as follows: m(1) = 6/100, m(2) = 33/100, m(3) = 11/100, m(4) = 37/100, m(5) = 8/100, m(6) = 5/100. Let E be the event "A card with an odd numbered rank is drawn," and F be the event "A card whose rank is less than or equal to 3 is drawn." (a) Compute P(E). (b) Compute P(F). (c) Before you compute P(Eʼn F), explain (in whole sentences) whether or not it is safe to use the formula P(E^ F) = P(E) · P(F) before knowing the answer to part (g). (d) Compute P(EΜF). (e) Compute P(F|E). (f) Compute P(E|F). (g) Based on some of your answers to parts (a), (b), (e), and (f), explain (in whole sentences) whether events E and F are independent or not. In your response, please write down which probabilities you are comparing, whether they are equal or not, and how their equality or difference shows that the events E and F are independent or not.
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:1. On this problem, give exact answers using both fractions and exact decimals.
One card is chosen from a set of cards that have ranks 1 to 6. Let X be the number
on the card chosen. The distribution function for picking the cards is given as follows:
m(1) = 6/100, m(2) = 33/100, m(3) = 11/100,
m(4) = 37/100, m(5) = 8/100, m(6) = 5/100.
Let E be the event "A card with an odd numbered rank is drawn," and
F be the event "A card whose rank is less than or equal to 3 is drawn."
(a) Compute P(E).
(b) Compute P(F).
(c) Before you compute P(Eʼn F), explain (in whole sentences) whether or not it is
safe to use the formula P(E^ F) = P(E) · P(F) before knowing the answer to
part (g).
(d) Compute P(EΜF).
(e) Compute P(F|E).
(f) Compute P(E|F).
(g) Based on some of your answers to parts (a), (b), (e), and (f), explain (in whole
sentences) whether events E and F are independent or not. In your response,
please write down which probabilities you are comparing, whether they are equal
or not, and how their equality or difference shows that the events E and F are
independent or not.
Expert Solution
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 1 steps with 1 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