Of nine executives in a business firm, three are married, four have never married, and two are divorced. Three of the executives are to be selected for promotion. Let Y, denote the number of married executives and Y, denote the number of never-married executives among the three selected for promotion. Assume that the three are randomly selected from the nine available. We determined that the joint probability distribution of Y,, the number of married executives, and Y,, the number of never-married executives, is given by GX---) (:) P(Y1, Y2) = - where y, and y, are integers, o s y, s 3, 0 s y, s 3, and 1 s y, + y, s 3. (a) Find the marginal probability distribution of Y,, the number of married executives among the three selected for promotion. (Enter your probabilities as fractions.) Y1 Marginal Probability (b) Find P(Y, = 1|Y, = 2). (Enter your probability as a fraction.) (c) If we let Y, denote the number of divorced executives among the three selected for promotion, then Y3 = 3 - Y, - Y2. Find P(Y = 1|Y, = 1). (Enter your probability as a fraction.)
Of nine executives in a business firm, three are married, four have never married, and two are divorced. Three of the executives are to be selected for promotion. Let Y, denote the number of married executives and Y, denote the number of never-married executives among the three selected for promotion. Assume that the three are randomly selected from the nine available. We determined that the joint probability distribution of Y,, the number of married executives, and Y,, the number of never-married executives, is given by GX---) (:) P(Y1, Y2) = - where y, and y, are integers, o s y, s 3, 0 s y, s 3, and 1 s y, + y, s 3. (a) Find the marginal probability distribution of Y,, the number of married executives among the three selected for promotion. (Enter your probabilities as fractions.) Y1 Marginal Probability (b) Find P(Y, = 1|Y, = 2). (Enter your probability as a fraction.) (c) If we let Y, denote the number of divorced executives among the three selected for promotion, then Y3 = 3 - Y, - Y2. Find P(Y = 1|Y, = 1). (Enter your probability as a fraction.)
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:Of nine executives in a business firm, three are married, four have never married, and two are divorced. Three of the executives are to be selected for promotion. Let Y, denote the
number of married executives and Y, denote the number of never-married executives among the three selected for promotion. Assume that the three are randomly selected from the
nine available.
We determined that the joint probability distribution of Y,, the number of married executives, and Y,, the number of never-married executives, is given by
P(Y1, Y2) =
(;)
where y, and y2 are integers, 0 sy, < 3, 0 s y2 < 3, and 1 s y, + Y2 < 3.
(a) Find the marginal probability distribution of Y,, the number of married executives among the three selected for promotion. (Enter your probabilities as fractions.)
Y1
2
3
Marginal Probability
(b) Find P(Y, = 1|Y, = 2). (Enter your probability as a fraction.)
(c) If we let Y3 denote the number of divorced executives among the three selected for promotion, then Y3 = 3 - Y, - Y2. Find P(Y, = 1|Y, = 1). (Enter your probability as a fraction.)
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 2 steps with 5 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