Math / Discrete

QuestionThe pattern of people picking up and returning rental cars at site $A, B$ , and $C$ , are given by the following transition matrix:
Pick up site $A B C$ $\left[\begin{array}{lll}0.5 & 0.2 & 0.4 \\ 0.2 & 0.2 & 0.3 \\ 0.3 & 0.6 & 0.3\end{array}\right] \begin{array}{ll}A \\ B \\ C\end{array}$ Returning Site
What does the entry in the first row third columin represent? [This question is based on your assigned pre-reading/prep for the upcoming Assignment] The probability that people will pick up their rental car at site C and return it to site A . The probability that people will pick up their rental car at site $C$ and return it to site $B$ . none of these The probability that people will pick up their rental car at site $A$ and return it to site $C$ .

Studdy Solution

STEP 1

What is this asking? Given a table showing how people pick up and return rental cars, what does the number in the top right corner mean? Watch out! Rows and columns can be tricky!
Make sure you're reading the table correctly.
The rows represent where people pick up the car, and the columns represent where they return it.

STEP 2

1. Understand the Matrix
2. Identify the Entry

STEP 3

Alright, so we've got this table, which is called a transition matrix.
It tells us how people move their rental cars between locations $\text{A}$ , $\text{B}$ , and $\text{C}$ .
The rows tell us the pick-up location, and the columns tell us the return location.

STEP 4

Let's look at an example.
The number in the first row and first column is $0.5$ .
This means that if someone picks up a car at location $\text{A}$ , there's a $0.5$ (or 50%) probability they'll return it to location $\text{A}$ .

STEP 5

The problem asks about the entry in the first row and third column.
This corresponds to picking up the car at location $\text{A}$ (first row) and returning it to location $\text{C}$ (third column).

STEP 6

The value in the first row and third column is $0.4$ .
This tells us that if someone picks up a car at location $\text{A}$ , there's a $0.4$ (or 40%) probability they'll return it to location $\text{C}$ .

STEP 7

The entry in the first row, third column represents the probability that people will pick up their rental car at site $A$ and return it to site $C$ .

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Studdy Solution

STEP 1

STEP 2

1. Understand the Matrix
2. Identify the Entry

STEP 3

Alright, so we've got this table, which is called a transition matrix.
It tells us how people move their rental cars between locations $\text{A}$ , $\text{B}$ , and $\text{C}$ .
The rows tell us the pick-up location, and the columns tell us the return location.

STEP 4

Let's look at an example.
The number in the first row and first column is $0.5$ .
This means that if someone picks up a car at location $\text{A}$ , there's a $0.5$ (or 50%) probability they'll return it to location $\text{A}$ .

STEP 5

The problem asks about the entry in the first row and third column.
This corresponds to picking up the car at location $\text{A}$ (first row) and returning it to location $\text{C}$ (third column).

STEP 6

The value in the first row and third column is $0.4$ .
This tells us that if someone picks up a car at location $\text{A}$ , there's a $0.4$ (or 40%) probability they'll return it to location $\text{C}$ .

STEP 7

The entry in the first row, third column represents the probability that people will pick up their rental car at site $A$ and return it to site $C$ .

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Studdy Solution

STEP 1

STEP 2

1. Understand the Matrix2. Identify the Entry

STEP 3

Alright, so we've got this table, which is called a **transition matrix**.It tells us how people move their rental cars between locations A\text{A}A, B\text{B}B, and C\text{C}C.The rows tell us the **pick-up location**, and the columns tell us the **return location**.

STEP 4

Let's look at an example.The number in the first row and first column is 0.50.50.5.This means that if someone picks up a car at location A\text{A}A, there's a 0.50.50.5 (or **50%**) probability they'll return it to location A\text{A}A.

STEP 5

The problem asks about the entry in the **first row** and **third column**.This corresponds to picking up the car at location A\text{A}A (first row) and returning it to location C\text{C}C (third column).

STEP 6

The value in the first row and third column is 0.40.40.4.This tells us that if someone picks up a car at location A\text{A}A, there's a 0.40.40.4 (or **40%**) probability they'll return it to location C\text{C}C.

STEP 7

The entry in the first row, third column represents the probability that people will pick up their rental car at site AAA and return it to site CCC.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. Understand the Matrix
2. Identify the Entry

Alright, so we've got this table, which is called a transition matrix.
It tells us how people move their rental cars between locations $\text{A}$ , $\text{B}$ , and $\text{C}$ .
The rows tell us the pick-up location, and the columns tell us the return location.

Let's look at an example.
The number in the first row and first column is $0.5$ .
This means that if someone picks up a car at location $\text{A}$ , there's a $0.5$ (or 50%) probability they'll return it to location $\text{A}$ .

The problem asks about the entry in the first row and third column.
This corresponds to picking up the car at location $\text{A}$ (first row) and returning it to location $\text{C}$ (third column).

The value in the first row and third column is $0.4$ .
This tells us that if someone picks up a car at location $\text{A}$ , there's a $0.4$ (or 40%) probability they'll return it to location $\text{C}$ .

The entry in the first row, third column represents the probability that people will pick up their rental car at site $A$ and return it to site $C$ .