What is the probability that both shots will be within 1 meter of the target, in the horizontal direction

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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Two archers will simultaneously shoot once at a target.

Let X, i = 1, 2, be marksman i's horizontal error, measured in meters. If the target's position is (a, b), and marksman i's shot ends up at (x, y), then Xi = (x - a).

These errors are modeled by X1 ~ N(0, 0.5) and X2 ~ N(0, 1).


What is the probability that both shots will be within 1 meter of the target, in the horizontal direction?

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