Q. 6.37 In Problem 6.5, calculate the co... [FREE SOLUTION]

91影视

A First Course in Probability

Sheldon M. Ross

$Math Studyset 91影视 Explanations$ Math

9th Edition 路 432 pages

ISBN: 9780321794772

Chapter 6: Q. 6.37 (page 273)

In Problem $6.5$ , calculate the conditional probability mass function of Y1 given that
(a) $Y_{2} = 1$
(b) $Y_{2} = 0$

Short Answer

Expert verified

$(a) P (Y_{1} = 0 鈭� Y_{2} = 1) = 0.8464 P (Y_{1} = 1 鈭� Y_{2} = 1) = 0.1536$

$(b) P (Y_{1} = 0 鈭� Y_{2} = 0) = 0.7702 P (Y_{1} = 1 鈭� Y_{2} = 0) = 0.2297$

Step by step solution

Given information (part a)

An urn contains $5$ white balls, $8$ red balls, and $3$ balls are to be chosen with replacement. the white balls have been numbered.

Compute the conditional probability that $Y_{1}$ given that $Y_{2} = 0$

role="math" localid="1647264516934" $P (Y_{1} 鈭� Y_{2} = 1) = \frac{P (Y_{1} 鈭� Y_{2} = 1)}{P (Y_{2} = 1)}$

Explanation (part a)

Substitute the values from the joint probability mass function.

For $Y_{1} = 0$

role="math" localid="1647265027423" $P (Y_{1} = 0 鈭� Y_{2} = 1) = \frac{P (Y_{1} = 0 鈭� Y_{2} = 1)}{P (Y_{2} = 1)} = \frac{0.1807}{0.2135} = 0.8464 F o r Y_{1} = 1 P (Y_{1} = 1 鈭� Y_{2} = 1) = \frac{P (Y_{1} = 1 鈭� Y_{2} = 1)}{P (Y_{2} = 1)} = \frac{0.0328}{0.2135} = 0.1536$

Given information (part b)

Compute the conditional probability that $Y_{1}$ given that $Y_{2} = 0$

$P (Y_{1} 鈭� Y_{2} = 0) = \frac{P (Y_{1} 鈭� Y_{2} = 0)}{P (Y_{2} = 0)}$

Explanation (part b)

Substitute the values from the joint probability mass function.

$F o r Y_{1} = 0$

$P (Y_{1} = 0 鈭� Y_{2} = 0) = \frac{P (Y_{1} = 0 鈭� Y_{2} = 0)}{P (Y_{2} = 0)} = \frac{0.6058}{0.7865} = 0.7702 F o r Y_{1} = 1 P (Y_{1} = 1 鈭� Y_{2} = 0) = \frac{P (Y_{1} = 1 鈭� Y_{2} = 0)}{P (Y_{2} = 0)} = \frac{0.1807}{0.7865} = 0.2297$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

In Problem $6.5$ , calculate the conditional probability mass function of Y1 given that
(a) $Y_{2} = 1$
(b) $Y_{2} = 0$

Short Answer

Step by step solution

Given information (part a)

Explanation (part a)

Given information (part b)

Explanation (part b)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Pure Maths

Probability and Statistics

Calculus

Mechanics Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

91影视

In Problem 6.5, calculate the conditional probability mass function of Y1 given that (a) Y2=1(b)Y2=0

Short Answer

Step by step solution

Given information (part a)

Explanation (part a)

Given information (part b)

Explanation (part b)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Pure Maths

Probability and Statistics

Calculus

Mechanics Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

In Problem $6.5$ , calculate the conditional probability mass function of Y1 given that
(a) $Y_{2} = 1$
(b) $Y_{2} = 0$