3 Challenging problems Some probability problems do not involve geometry directly, but can be solved nicely using geometric repre- sentations. Let's start from playing a game. 4. You and I both randomly choose an integer from {1,2,3, 4, 5, 6, 7, 8, 9, 10}. If your number is no more than 2 away from my number, you win $1,000! What is your probability of winning? (Assume you make wise choices.)

A First Course in Probability (10th Edition)
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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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3 Challenging problems
Some probability problems do not involve geometry directly, but can be solved nicely using geometric repre-
sentations. Let's start from playing a game.
4. You and I both randomly choose an integer from {1,2,3, 4, 5, 6, 7, 8,9, 10}. If your number is no more than
2 away from my number, you win $1,000! What is your probability of winning? (Assume you make wise
choices.)
5. Let's change the game a little. Now instead of choosing the integers, you can I both randomly choose a real
number in [1,10]. And the rule is still that, if your number is no more than 2 away from my number, you win.
Now what is your probability of winning? (Assume you still make wise choices.)
4
Transcribed Image Text:3 3 Challenging problems Some probability problems do not involve geometry directly, but can be solved nicely using geometric repre- sentations. Let's start from playing a game. 4. You and I both randomly choose an integer from {1,2,3, 4, 5, 6, 7, 8,9, 10}. If your number is no more than 2 away from my number, you win $1,000! What is your probability of winning? (Assume you make wise choices.) 5. Let's change the game a little. Now instead of choosing the integers, you can I both randomly choose a real number in [1,10]. And the rule is still that, if your number is no more than 2 away from my number, you win. Now what is your probability of winning? (Assume you still make wise choices.) 4
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