Suppose your email prompts you to create a new password. It must be 8 characters long, with the first three being letters, and the last five being digits 0-9. How many possible passwords can you create? **Transcription for Educational Website: Dice Probability Questions**---**1. Question:**Two four-sided dice are rolled, and the numbers face up are recorded.a. What is the sample space? *List the outcomes, not the number of outcomes.*b. Find the probability that you roll a total that is even.c. Find the probability that you roll at least one 2.---**Explanation:**- *Sample Space:* The sample space for two four-sided dice includes all possible outcomes of rolling the dice. Each die has four faces, numbered 1 through 4. To list the sample space, enumerate all possible combinations of the results from both dice: (1,1), (1,2), (1,3), (1,4), (2,1), ..., (4,4).- *Probability of an Even Total:* Determine the outcomes where the sum of the numbers on both dice is even (e.g., 2, 4, 6, etc.) and calculate the probability.- *Probability of Rolling at Least One 2:* Identify all the scenarios where at least one die shows the number 2 and calculate the probability.---**Note:** For educational purposes, students should attempt to derive the sample space and solve each probability-related question by listing potential outcomes and using probability formulas.

Answered: Suppose yor characters long, with th…

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...

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Suppose your email prompts you to create a new password. It must be 8 characters long, with the first three being letters, and the last five being digits 0-9. How many possible passwords can you create?

**Transcription for Educational Website: Dice Probability Questions**

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**1. Question:**

Two four-sided dice are rolled, and the numbers face up are recorded.

a. What is the sample space? *List the outcomes, not the number of outcomes.*

b. Find the probability that you roll a total that is even.

c. Find the probability that you roll at least one 2.

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**Explanation:**

- *Sample Space:* The sample space for two four-sided dice includes all possible outcomes of rolling the dice. Each die has four faces, numbered 1 through 4. To list the sample space, enumerate all possible combinations of the results from both dice: (1,1), (1,2), (1,3), (1,4), (2,1), ..., (4,4).

- *Probability of an Even Total:* Determine the outcomes where the sum of the numbers on both dice is even (e.g., 2, 4, 6, etc.) and calculate the probability.

- *Probability of Rolling at Least One 2:* Identify all the scenarios where at least one die shows the number 2 and calculate the probability.

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**Note:** For educational purposes, students should attempt to derive the sample space and solve each probability-related question by listing potential outcomes and using probability formulas.

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Given, the email prompts to create a new password which is 8 characters long with first three characters being letters and last five characters being digits from 0-9.

Now, there are 26 letters and 10 digits.

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