1. Explain the probability distribution for each die.-calculate expected value and variance for each die If you roll a 1, you get $1.If you roll a 2, you get $2.If you roll a 3, you get $0. (That's right: you get no money.)If you roll a 4, you get $4.If you roll a 5, you get $5.If you roll a 6, you get $6. Scarlett has two six-sided dice. One is red, one is blue, and both are loaded. (If a die is"loaded," it is not "fair." A "fair" die has probability 1/6 of landing on any given side.) Inparticular, the red die is weighted such that:Odd numbers are twice as likely as evens.1, 3, and 5 are equally likely.2, 4, and 6 are equally likely.The blue die is weighted such that:1 and 5 are equally likely.2 and 4 are equally likely.3 and 6 are equally likely.3 is twice as likely as 2.2 is twice as likely as 1.Scarlett has three games for you to play.In the first game, you get to choose a die (red or blue, with the probabilities describedabove) and then roll it once.If you roll a 1, you get $1.If you roll a 2, you get $2.• If you roll a 3, you get $3.If you roll a 4, you get $4.If you roll a 5, you get $5.• If you roll a 6, you get $6.In the second game, you get to choose a die (red or blue, with the probabilitiesdescribed above) and then roll it four times.If any of your rolls resultin a 3, you get $0. (That's right: you get no money.)If none of your rolls resultin a 3, you get $3.In the third game, you get to choose a die (red or blue, with the probabilities describedabove) and then roll it once.

Name: 1. Explain the probability distribution for each die.-calculate expect
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: 1. Explain the probability distribution for each die.-calculate expected value and variance for each die If you roll a 1, you get $1.If you roll a 2, you get $2.If you roll a 3, you get $0. (That's right: you get no money.)If you roll a 4, you get $4

Answered: Explain the probability distribution…

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...

See similar textbooks

Related questions

Concept explainers

Topic Video

Question

1. Explain the probability distribution for each die.

-calculate expected value and variance for each die

If you roll a 1, you get $1.
If you roll a 2, you get $2.
If you roll a 3, you get $0. (That's right: you get no money.)
If you roll a 4, you get $4.
If you roll a 5, you get $5.
If you roll a 6, you get $6.

Scarlett has two six-sided dice. One is red, one is blue, and both are loaded. (If a die is
"loaded," it is not "fair." A "fair" die has probability 1/6 of landing on any given side.) In
particular, the red die is weighted such that:
Odd numbers are twice as likely as evens.
1, 3, and 5 are equally likely.
2, 4, and 6 are equally likely.
The blue die is weighted such that:
1 and 5 are equally likely.
2 and 4 are equally likely.
3 and 6 are equally likely.
3 is twice as likely as 2.
2 is twice as likely as 1.
Scarlett has three games for you to play.
In the first game, you get to choose a die (red or blue, with the probabilities described
above) and then roll it once.
If you roll a 1, you get $1.
If you roll a 2, you get $2.
• If you roll a 3, you get $3.
If you roll a 4, you get $4.
If you roll a 5, you get $5.
• If you roll a 6, you get $6.
In the second game, you get to choose a die (red or blue, with the probabilities
described above) and then roll it four times.
If any of your rolls resultin a 3, you get $0. (That's right: you get no money.)
If none of your rolls resultin a 3, you get $3.
In the third game, you get to choose a die (red or blue, with the probabilities described
above) and then roll it once.

Expert Solution

Step 1

As we are authorized to answer only 1 question and that you haven't specified which of the questions you want the solutions for, therefore, the first question is being answered for now. Requesting you to re-upload the remaining questions for the answers to them.

Let X : number occurs on the die

X={1,2,3,4,5,6}

Let Y : the prize money

Step 2

The probability distribution of X for each die is given by:

X	P(x)
1	$\frac{1}{6}$
2	$\frac{1}{6}$
3	$\frac{1}{6}$
4	$\frac{1}{6}$
5	$\frac{1}{6}$
6	$\frac{1}{6}$

The probability distribution of Y and expected Y is given as:

Y (in $)	P(Y)	E(Y) (in $)
1	$\frac{1}{6}$	$\frac{1}{6}$
2	$\frac{1}{6}$	$\frac{1}{3}$
0	$\frac{1}{6}$	$0$
4	$\frac{1}{6}$	$\frac{2}{3}$
5	$\frac{1}{6}$	$\frac{5}{6}$
6	$\frac{1}{6}$	$1$
Total	1	3

Where the expected prize money is given by :

$E (y) = \sum_{y} y \times P (y) = 3$

Therefore, the expected value for each die is given as:

Die	Expected Value (in $)
1
2
3	0
4
5
6	1
Total	3

Step by step

Solved in 4 steps

Knowledge Booster

$Discrete Probability Distributions$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.